[Problem 4] Consider the sequence of integers 0, 1, 1, 7, 13, 55, 133, 463.. a) find the recursive function and initial conditions which generates them b) using the solution in part a), find the closed form solution for this sequence c) implement the recursive function in Python
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- (C Language) Write a recursive function called DrawTriangle() that outputs lines of '*' to form a right side up isosceles triangle. Function DrawTriangle() has one parameter, an integer representing the base length of the triangle. Assume the base length is always odd and less than 20. Output 9 spaces before the first '*' on the first line for correct formatting. Hint: The number of '*' increases by 2 for every line drawn.(C Language) Write a recursive function called PrintNumPattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until a negative value is reached, and then continually add the second integer until the first integer is again reached. For this lab, do not end output with a newline.Question 1: Tracing Recursive functions The solution can be handwrittena) Trace the following recursive method for the function call “multiplyDigits(58746)” and show the output result.
- (C Language) Write a recursive function called DigitCount() that takes a non-negative integer as a parameter and returns the number of digits in the integer. Hint: The digit count increases by 1 whenever the input number is divided by 10.- Writea C++ code (using a function) to read an integer value time (T) and convert it to equivalent minutes (M) and hours (HE - Write a C++ code using recursive function to find the cube of n number.fl(2) Create an iterative and a recursive function in pseudo-code which calculates the ele- ments of the sequence given on the following drawing. The green numbers mean the index (Oth element, 1st element, 2nd element, etc.) and the black mean the actual va- lue. Note: I did not calculate all the values, just the "necessary" ones.: 27 2 2 7
- Python program (recursive function) A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. Write a python recursive functionprod that takes x as an argument, and returns the result where, result=1*1/2*1/3*….*1/n Include a screenshot that shows a python program that uses the above function and prints the rounded result to three decimal placesafter prompting the user to enter a number, x. Use x=3. N.B: The code should be included please.(C++) Write a recursive function to print the following pattern.Example:Enter any number = 442 21 31 1 21 1 1 1(Recursive Exponentiation) Write a recursive function power(base, exponent) that wheninvoked returnsbaseexponentFor example, power(3, 4) = 3 * 3 * 3 * 3. Assume that exponent is an integer greater than or equalto 1. Hint: The recursion step would use the relationshipbaseexponent = base * baseexponent–1and the terminating condition occurs when exponent is equal to 1 becausebase1 = base
- (Recursive Sequential Search) The sequential search algorithm given in nonrecursive. Write and implement a recursive version of the sequential search algorithm.(Recursive Greatest Common Divisor) The greatest common divisor of integers x and y isthe largest integer that evenly divides both x and y. Write a recursive function gcd that returns thegreatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equalto 0, then gcd(x, y) is x; otherwise gcd(x, y) is gcd(y, x % y), where % is the remainder operator.Python only* Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle Do not use any kind of loop Within the definition of…