A025436 Number of partitions of n into 3 distinct squares.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 1, 1, 0, 2, 2, 0, 0, 3, 1, 0, 1, 2, 1, 0, 0, 1, 3, 1, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 3, 3, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 4, 0, 0, 2, 2, 2, 1

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Programs

Maple

N:= 1000; # to get a(0) to a(N)
A:= Vector(N+1);
for a from 2 to floor(sqrt(N)) do
   for b from 1 to min(a-1,floor(sqrt(N-a^2))) do
      for c from 0 to min(b-1, floor(sqrt(N-a^2-b^2))) do
         x:= a^2 + b^2 + c^2;
         A[x+1]:= A[x+1]+1
od od od:
convert(A,list); # Robert Israel, Nov 11 2015

Mathematica

n = 100; Clear[A]; A[] = 0; For[a = 2, a <= Floor[Sqrt[n]], a++, For[b = 1, b <= Min[a-1, Floor[Sqrt[n-a^2]]], b++, For[c = 0, c <= Min[b-1, Floor[Sqrt[n-a^2-b^2]]], c++, x = a^2 + b^2 + c^2; A[x+1] = A[x+1]+1]]]; Array[A, n] (* _Jean-François Alcover, Nov 11 2015, adapted from Robert Israel's Maple script *)

Formula

G.f.: (1+theta_3(x))^3/48 - (1+theta_3(x))*(1+theta_3(x^2))/8 + (1 + theta_3(x^3))/6, where theta_3 is a Jacobi theta function. - Robert Israel, Nov 11 2015