A178898 - OEIS

%I #7 Jul 18 2013 06:22:59

%S 0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,4,3,6,7,13,7,16,14,21,21,27,24,31,35,

%T 43,43,60,51,66,61,88,83,105,91,137,116,124,140,185,143,195,187,233,

%U 197,266,220,317,283,318,317,371,331,433,404,476,450,529,427,620,543,616

%N a(n) = number of ways in which n^2 can be expressed as the sum of five different squares.

%C a(n) ignores the order of the five squares. If we count all 5-plets whose squares sum to a square, including repetitions, then the limit as n goes to infinity of the ratio of this number to a(n) is 5/4.

%F a(n) = A025444(n^2). [From _R. J. Mathar_, Oct 18 2010]

%e For n=17 a(17)=3 since 17^2 can be expressed as the sum of 5 different squares in 3 ways: 17^2 = 14^2+8^2+4^2+3^2+2^2 = 13^2+8^2+6^2+4^2+2^2 = 12^2+10^2+5^2+4^2+2^2.

%K nonn

%O 1,15

%A _Carmine Suriano_, Jun 21 2010