A132432 Number of different values of i^2+j^2+k^2+l^2+m^2 for i,j,k,l,m in [0,n].

1, 6, 18, 38, 66, 99, 147, 201, 262, 332, 411, 498, 601, 702, 819, 946, 1078, 1221, 1375, 1533, 1703, 1882, 2076, 2264, 2479, 2691, 2922, 3159, 3403, 3655, 3924, 4193, 4478, 4770, 5071, 5376, 5705, 6032, 6372, 6719, 7081, 7448, 7828, 8214, 8616, 9017, 9438

Offset: 0

Author

Jonathan Vos Post, Nov 13 2007, Nov 14 2007

Keywords

• easy
• nonn

Examples

			a(3) = 18 because the 18 different sums of 5 squares of integers from 0 to 2 are: {20, 17, 16, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0} by permutations of 2^2 + 2^2 + 2^2 + 2^2 + 2^2 = 20; 2^2 + 2^2 + 2^2 + 2^2 + 1^2 = 17; 2^2 + 2^2 + 2^2 + 2^2 + 0^2 = 16; 2^2 + 2^2 + 2^2 + 1^2 + 1^2 = 14; 2^2 + 2^2 + 2^2 + 1^2 + 0^2 = 13; 2^2 + 2^2 + 2^2 + 0^2 + 0^2 = 12; 2^2 + 2^2 + 1^2 + 1^2 + 1^2 = 11; 2^2 + 2^2 + 1^2 + 1^2 + 0^2 = 10; 2^2 + 2^2 + 1^2 + 0^2 + 0^2 = 9; 2^2 + 2^2 + 0^2 + 0^2 + 0^2 = 2^2 + 1^2 + 1^2 + 1^2 + 1^2 = 8; 2^2 + 1^2 + 1^2 + 1^2 + 0^2 = 7; 2^2 + 1^2 + 1^2 + 0^2 + 0^2 = 6; 2^2 + 1^2 + 0^2 + 0^2 + 0^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 = 5; 2^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1^2 + 1^2 + 1^2 + 1^2 + 0^2 = 4; 1^2 + 1^2 + 1^2 + 0^2 + 0^2 = 3; 1^2 + 1^2 + 0^2 + 0^2 + 0^2 = 2; 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1; 0^2 + 0^2 + 0^2 + 0^2 + 0^2 = 0.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A034966, A047800, A047801.

Programs

Maple

S:= proc(k,n) option remember;
if k = 0 or n = 0 then {0} else
`union`(seq(map(`+`,procname(j,n-1),(k-j)*n^2),j=1..k-1),
{k*n^2},procname(k,n-1)) fi end proc:
seq(nops(S(5,n)),n=0..100); # Robert Israel, Jun 28 2018

Mathematica

Table[Length@ Union@Flatten@ Table[i^2 + j^2 + k^2 + l^2 + m^2, {i, 0, n}, {j, i, n}, {k, j, n}, {l, k, n}, {m, l, n}], {n, 0, 49}]

Extensions

Offset corrected by Giovanni Resta, Jun 18 2016