Combinations without using nchoosek
You have to generate a matrix with all possible combinations of n elements *taken 2* at a time, *without using nchoosek(1:n,2)* ...
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Fibonacci sequence
Calculate the nth Fibonacci number.
Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...
Examples:
Inpu...
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Compute Fibonacci Number
Compute the _n_-th Fibonacci Number
f(0) = 0,
f(1) = 1,
f(2) = 1,
f(3) = 2, ...
f(42) = 267914296
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Determine if given number is perfect
A number is <http://en.wikipedia.org/wiki/Perfect_number perfect> if it is equal to the sum of its factors, excluding itself.
...
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That's some divisor you've got there...
Given a positive integer x, calculate the sum of all of the divisors of the number. Please include the number itself in your fi...
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Divisors of an integer
Given a number N, return a vector V of all integers that divide N.
For example,
N = 10
Then
V=[1 2 5 10]
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Amicable numbers
Test whether two numbers are <https://en.wikipedia.org/wiki/Amicable_numbers amicable>, meaning that the sum of the proper divis...
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prime to each other
Given two integers n1, n2 greater than 1, find out if they have common divisors or are prime to each other. Return "true" if the...
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Determine if input is a perfect number
A <http://en.wikipedia.org/wiki/Perfect_number/ perfect number> occurs whent the sum of all divisors of a positive integer, exce...
Mirror Image matrix across anti-diagonal
Given an input number x, create a mirror image matrix 'Y' across the anti-diagonal. For example, if x=3,
Y = [1 2 3;
...
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Generate this matrix
Generate the following matrix.
n = 2;
out = [-4 -3 -2 -1 0
-3 -2 -1 0 1
-...
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ZigZag matrix with reflected format
ZigZag MATRIX with REFLECTED format.
We have only input x. We have to create a matrix in the following pattern.
input n=5...
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Pascal's Matrix
Given an integer n ≥ 0, generate the ( _n_+1) × ( _n_+1) lower triangular <http://en.wikipedia.org/wiki/Pascal_matrix P...
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Symmetric matrix
You must create a n-by-n *symmetric* matrix such that A(row,col) = row/col for col >= row.
Example if n =3 :
output is :
...
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Make a Star Pyramid
Create a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done...