A348541 Number of partitions of n into 3 parts (r,s,t) such that n | (r^2 + s^2 + t^2).

0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 2, 2, 4, 1, 1, 0, 3, 3, 0, 4, 0, 0, 6, 2, 8, 4, 4, 0, 2, 5, 5, 1, 0, 1, 3, 6, 12, 7, 1, 0, 14, 7, 0, 1, 0, 0, 6, 11, 8, 1, 8, 0, 12, 0, 17, 10, 0, 0, 2, 10, 20, 10, 5, 2, 2, 11, 0, 1, 4, 0, 12, 12, 24, 9, 12, 1, 26, 13, 1, 7, 0, 0, 14, 0, 28, 1, 1

Offset: 1

Author

Wesley Ivan Hurt, Oct 21 2021

Keywords

• nonn

Examples

			a(6) = 2; 6 | (1^2 + 1^2 + 4^2) = 18 and 6 | (2^2 + 2^2 + 2^2) = 12, so a(6) = 2.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A069905.

Programs

Mathematica

c[n_] := 1 - Ceiling[n] + Floor[n]; a[n_] := Sum[c[(j^2 + i^2 + (n - i - j)^2)/n], {j, 1, Floor[n/3]}, {i, j, Floor[(n - j)/2]}]; Array[a, 100] (* Amiram Eldar, Oct 22 2021 *)

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c((j^2 + i^2 + (n-i-j)^2)/n), where c(n) = 1 - ceiling(n) + floor(n).