cp's OEIS Frontend

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].

%I A132432 #11 Jun 28 2018 21:45:01
%S A132432 1,6,18,38,66,99,147,201,262,332,411,498,601,702,819,946,1078,1221,
%T A132432 1375,1533,1703,1882,2076,2264,2479,2691,2922,3159,3403,3655,3924,
%U A132432 4193,4478,4770,5071,5376,5705,6032,6372,6719,7081,7448,7828,8214,8616,9017,9438
%N 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].
%H A132432 Robert Israel, <a href="/A132432/b132432.txt">Table of n, a(n) for n = 0..500</a>
%e A132432 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.
%p A132432 S:= proc(k,n) option remember;
%p A132432 if k = 0 or n = 0 then {0} else
%p A132432 `union`(seq(map(`+`,procname(j,n-1),(k-j)*n^2),j=1..k-1),
%p A132432 {k*n^2},procname(k,n-1)) fi end proc:
%p A132432 seq(nops(S(5,n)),n=0..100); # _Robert Israel_, Jun 28 2018
%t A132432 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}]
%Y A132432 Cf. A034966, A047800, A047801.
%K A132432 easy,nonn
%O A132432 0,2
%A A132432 _Jonathan Vos Post_, Nov 13 2007, Nov 14 2007
%E A132432 Offset corrected by _Giovanni Resta_, Jun 18 2016