CodeCogs

Returns the number of alternating sign matrices of the given order.

View versions (1)

Interface

#include <codecogs/maths/combinatorics/sequences/asm_number.h>

using namespace Maths::Combinatorics::Sequences;

int asm_number(int n)

A direct formula for calculating the number of alternating sign matrices of order n is:

$\prod_{i = 0}^{n - 1} \frac{(3i + 1)!}{(n + i)!}$

(1)

References

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

Example 1

#include <codecogs/maths/combinatorics/sequences/asm_number.h>
#include <iostream>
int main()
{
  for (int i = 0; i < 10; i++)
    std::cout << i << " " << Maths::Combinatorics::Sequences::asm_number(i) << std::endl;
  return 0;
}

Output:

0 1
1 1
2 2
3 7
4 42
5 429
6 7436
7 218348
8 10850216
9 188958604

Parameters

the order of the matrices

Returns

the number of alternating matrices of order n

Interactive Calculator

Result –

ASM_Number

Interface

References

Example 1

Parameters

Returns