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%I #8 Jun 19 2016 13:24:43
%S 1,7,22,47,82,124,183,250,326,414,513,621,749,874,1018,1176,1338,1515,
%T 1706,1899,2110,2331,2568,2806,3066,3324,3612,3903,4201,4513,4841,
%U 5173,5523,5882,6248,6626,7026,7433,7842,8271,8715
%N Number of different values of i^2+j^2+k^2+l^2+m^2+n^2 for i,j,k,l,m,n in [0,n].
%C Number of distinct sums of 6 squares of integers from 0 through n.
%e a(1) = 7 because the 7 distinct sums of squares from 0 through 1 are permutations of 1^2 + 1^1 + 1^2 + 1^2 + 1^2 + 1^2 = 6; 1^1 + 1^2 + 1^2 + 1^2 + 1^2 + 0^2 = 5; 1^1 + 1^2 + 1^2 + 1^2 + 0^2 + 0^2 = 4; 1^1 + 1^2 + 1^2 + 0^2 + 0^2 + 0^2 = 3; 1^1 + 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 2; 1^1 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1; 0^2 + 0^1 + 0^2 + 0^2 + 0^2 + 0^2 = 0.
%t Table[Length@ Union@Flatten@ Table[i^2 + j^2 + k^2 + l^2 + m^2 + n^2, {i, 0, p}, {j, i, p}, {k, j, p}, {l, k, p}, {m, l, p}, {n, m, p}], {p, 0, 40}]
%Y Cf. A034966, A047800, A047801, A132432.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Nov 13 2007, Nov 14 2007
%E Offset corrected by _Giovanni Resta_, Jun 19 2016
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