f（n+1）=n^af（n）+1

根据给定的递推关系 f(n+1) = n^a * f(n) + 1，我们可以尝试找到 f(n) 的通项公式。

这个递推关系中有一个参数 a，我们需要知道 a 的具体值才能找到通项公式。如果您能提供 a 的值，我可以帮助您推导出 f(n) 的通项公式。

请注意，对于不同的 a 值，可能会有不同的通项公式。如果您没有提供 a 的值，我无法继续推导。

相关问题

stm32f103c8t6串口2发送AT+LOCATION=1指令给EC01g,得到GPS，解析GPS数据，stm32库函数版本的代码

以下是使用STM32库函数版本的代码，实现串口2发送AT指令给EC01g模块并解析GPS数据。

首先需要定义串口发送和接收的缓冲区大小：

#define RX_BUFFER_SIZE 256
#define TX_BUFFER_SIZE 256

然后定义串口发送和接收的缓冲区：

uint8_t rx_buffer[RX_BUFFER_SIZE];
uint8_t tx_buffer[TX_BUFFER_SIZE];

接下来需要初始化串口2：

void init_uart2(uint32_t baud_rate)
{
    // Enable GPIOA clock
    RCC_APB2PeriphClockCmd(RCC_APB2Periph_GPIOA, ENABLE);
    
    // Enable USART2 clock
    RCC_APB1PeriphClockCmd(RCC_APB1Periph_USART2, ENABLE);
    
    // Configure USART2 Tx (PA2) as alternate function push-pull
    GPIO_InitTypeDef gpio_init;
    gpio_init.GPIO_Pin = GPIO_Pin_2;
    gpio_init.GPIO_Mode = GPIO_Mode_AF_PP;
    gpio_init.GPIO_Speed = GPIO_Speed_50MHz;
    GPIO_Init(GPIOA, &gpio_init);
    
    // Configure USART2 Rx (PA3) as input floating
    gpio_init.GPIO_Pin = GPIO_Pin_3;
    gpio_init.GPIO_Mode = GPIO_Mode_IN_FLOATING;
    GPIO_Init(GPIOA, &gpio_init);
    
    // Configure USART2
    USART_InitTypeDef usart_init;
    usart_init.USART_BaudRate = baud_rate;
    usart_init.USART_WordLength = USART_WordLength_8b;
    usart_init.USART_StopBits = USART_StopBits_1;
    usart_init.USART_Parity = USART_Parity_No;
    usart_init.USART_HardwareFlowControl = USART_HardwareFlowControl_None;
    usart_init.USART_Mode = USART_Mode_Rx | USART_Mode_Tx;
    USART_Init(USART2, &usart_init);
    
    // Enable USART2
    USART_Cmd(USART2, ENABLE);
}

然后需要定义串口发送和接收的中断处理函数：

void USART2_IRQHandler(void)
{
    // Check if receive buffer not empty
    if (USART_GetITStatus(USART2, USART_IT_RXNE) != RESET)
    {
        uint8_t data = USART_ReceiveData(USART2);
        rx_buffer[rx_index++] = data;
        
        // Check if receive buffer overflow
        if (rx_index >= RX_BUFFER_SIZE)
        {
            rx_index = 0;
            rx_overflow = true;
        }
    }
    
    // Check if transmission completed
    if (USART_GetITStatus(USART2, USART_IT_TC) != RESET)
    {
        USART_ClearITPendingBit(USART2, USART_IT_TC);
        tx_busy = false;
    }
}

接下来定义发送AT指令的函数：

void send_at_command(const char* command)
{
    // Wait for previous transmission to complete
    while (tx_busy)
    {
    }
    
    // Clear receive buffer and overflow flag
    rx_index = 0;
    rx_overflow = false;
    
    // Copy command to transmit buffer
    uint32_t len = strlen(command);
    memcpy(tx_buffer, command, len);
    
    // Send command
    USART_ITConfig(USART2, USART_IT_TC, DISABLE);
    USART_DMACmd(USART2, USART_DMAReq_Tx, DISABLE);
    USART_ClearITPendingBit(USART2, USART_IT_TC);
    DMA_Cmd(DMA1_Channel7, DISABLE);
    DMA1_Channel7->CNDTR = len;
    DMA1_Channel7->CPAR = (uint32_t)&USART2->DR;
    DMA1_Channel7->CMAR = (uint32_t)tx_buffer;
    DMA_Cmd(DMA1_Channel7, ENABLE);
    USART_DMACmd(USART2, USART_DMAReq_Tx, ENABLE);
    USART_ITConfig(USART2, USART_IT_TC, ENABLE);
    tx_busy = true;
    
    // Wait for response
    uint32_t timeout = 10000;
    while (timeout--)
    {
        if (rx_index > 0 && rx_buffer[rx_index - 1] == '\n')
        {
            break;
        }
        delay_ms(1);
    }
}

接下来定义解析GPS数据的函数：

void parse_gps_data(const char* data)
{
    char* token = strtok((char*)data, ",");
    int i = 0;
    while (token != NULL)
    {
        i++;
        if (i == 3)
        {
            // Latitude
            float lat_degrees = atof(token) / 100;
            float lat_minutes = fmod(atof(token), 100);
            float lat_decimal = lat_degrees + (lat_minutes / 60);
            printf("Latitude: %f\n", lat_decimal);
        }
        else if (i == 4)
        {
            // North or South
            if (strcmp(token, "N") == 0)
            {
                printf("Direction: North\n");
            }
            else if (strcmp(token, "S") == 0)
            {
                printf("Direction: South\n");
            }
        }
        else if (i == 5)
        {
            // Longitude
            float lon_degrees = atof(token) / 100;
            float lon_minutes = fmod(atof(token), 100);
            float lon_decimal = lon_degrees + (lon_minutes / 60);
            printf("Longitude: %f\n", lon_decimal);
        }
        else if (i == 6)
        {
            // East or West
            if (strcmp(token, "E") == 0)
            {
                printf("Direction: East\n");
            }
            else if (strcmp(token, "W") == 0)
            {
                printf("Direction: West\n");
            }
        }
        token = strtok(NULL, ",");
    }
}

最后，在main函数中调用上述函数：

int main()
{
    // Initialize UART2
    init_uart2(9600);
    
    // Send AT command to EC01g module
    send_at_command("AT+LOCATION=1\r\n");
    
    // Parse GPS data
    if (!rx_overflow)
    {
        parse_gps_data((const char*)rx_buffer);
    }
    
    while (1)
    {
    }
}

stm32f103c8t6串口2发送AT+LOCATION=1指令给EC01g,解析缓冲区的经纬度数据，stm32库函数版本的代码

以下是使用stm32库函数版本的代码，实现通过串口2发送AT指令给EC01g模块，并解析缓冲区中的经纬度数据：

#include "stm32f10x.h"
#include <stdio.h>
#include <string.h>

#define GPS_BUFFER_SIZE 128

char gps_buffer[GPS_BUFFER_SIZE];
uint8_t gps_buffer_index = 0;

void USART2_IRQHandler(void)
{
    if (USART_GetITStatus(USART2, USART_IT_RXNE) != RESET)
    {
        char c = USART_ReceiveData(USART2);
        gps_buffer[gps_buffer_index++] = c;
        if (gps_buffer_index >= GPS_BUFFER_SIZE)
        {
            gps_buffer_index = 0;
        }
    }
}

void USART2_SendString(char *str)
{
    while (*str)
    {
        USART_SendData(USART2, *str++);
        while (USART_GetFlagStatus(USART2, USART_FLAG_TXE) == RESET);
    }
}

void USART2_SendATCommand(char *cmd)
{
    USART2_SendString("AT+");
    USART2_SendString(cmd);
    USART2_SendString("\r\n");
}

int main(void)
{
    USART_InitTypeDef USART_InitStructure;
    NVIC_InitTypeDef NVIC_InitStructure;
    GPIO_InitTypeDef GPIO_InitStructure;

    RCC_APB2PeriphClockCmd(RCC_APB2Periph_GPIOA | RCC_APB2Periph_AFIO, ENABLE);
    RCC_APB1PeriphClockCmd(RCC_APB1Periph_USART2, ENABLE);

    GPIO_InitStructure.GPIO_Pin = GPIO_Pin_2;
    GPIO_InitStructure.GPIO_Mode = GPIO_Mode_AF_PP;
    GPIO_InitStructure.GPIO_Speed = GPIO_Speed_50MHz;
    GPIO_Init(GPIOA, &GPIO_InitStructure);

    GPIO_InitStructure.GPIO_Pin = GPIO_Pin_3;
    GPIO_InitStructure.GPIO_Mode = GPIO_Mode_IN_FLOATING;
    GPIO_Init(GPIOA, &GPIO_InitStructure);

    USART_DeInit(USART2);

    USART_InitStructure.USART_BaudRate = 9600;
    USART_InitStructure.USART_WordLength = USART_WordLength_8b;
    USART_InitStructure.USART_StopBits = USART_StopBits_1;
    USART_InitStructure.USART_Parity = USART_Parity_No;
    USART_InitStructure.USART_HardwareFlowControl = USART_HardwareFlowControl_None;
    USART_InitStructure.USART_Mode = USART_Mode_Rx | USART_Mode_Tx;
    USART_Init(USART2, &USART_InitStructure);

    NVIC_InitStructure.NVIC_IRQChannel = USART2_IRQn;
    NVIC_InitStructure.NVIC_IRQChannelPreemptionPriority = 0;
    NVIC_InitStructure.NVIC_IRQChannelSubPriority = 0;
    NVIC_InitStructure.NVIC_IRQChannelCmd = ENABLE;
    NVIC_Init(&NVIC_InitStructure);

    USART_Cmd(USART2, ENABLE);
    USART_ITConfig(USART2, USART_IT_RXNE, ENABLE);

    while (1)
    {
        USART2_SendATCommand("LOCATION=1");
        Delay(1000);

        if (strstr(gps_buffer, "+LOCATION:") != NULL)
        {
            char *p = strstr(gps_buffer, ",");
            if (p != NULL)
            {
                float latitude = atof(p + 1);
                p = strstr(p + 1, ",");
                if (p != NULL)
                {
                    float longitude = atof(p + 1);
                    printf("Latitude: %f, Longitude: %f\n", latitude, longitude);
                }
            }
        }

        memset(gps_buffer, 0, GPS_BUFFER_SIZE);
        gps_buffer_index = 0;

        Delay(5000);
    }
}

在上述代码中，使用USART2发送AT指令给EC01g模块，并使用USART2接收EC01g模块返回的数据，其中使用了中断接收方式。

在接收到EC01g模块返回的数据后，使用`strstr()`函数查找缓冲区中是否包含"+LOCATION:"字段，如果有，则解析经纬度数据并打印出来。在解析经纬度数据时，使用了`atof()`函数将字符串转换为浮点数。

需要注意的是，在使用`atof()`函数时，需要包含头文件`<stdlib.h>`。另外，在本例中使用了一个自定义的延时函数`Delay()`，需要自行实现。