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

0,27

Links

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

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

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 *)

Crossrefs

Sequence in context: A079181 A093693 A224447 * A170976 A134109 A325227

Adjacent sequences: A025433 A025434 A025435 * A025437 A025438 A025439

Keyword

nonn

Author

David W. Wilson

Status

approved