cp's OEIS Frontend

A223726 Multiplicities for A004433: sum of four distinct nonzero squares.

%I A223726 #7 Apr 07 2013 10:59:42
%S A223726 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,2,1,1,2,2,1,2,3,2,1,1,1,
%T A223726 3,2,1,3,1,1,1,2,1,1,1,2,1,5,1,2,3,1,1,2,3,1,2,1,1,2,4,2,1,2,3,1,5,2,
%U A223726 2,2,2,3,4,3,1,4,1,1,4,2,2,2,5,3,1,6,3,3,1,2,1,1,4,4,1,2,5,1,3,7,3,2,3,4
%N A223726 Multiplicities for A004433: sum of four distinct nonzero squares.
%C A223726 The number A004433(n) can be partitioned into four distinct parts, each of which is a nonzero square, and a(n) gives the multiplicity which is the number of different partitions of this type.
%F A223726 a(n) = k if there are k different quadruples [s(1),s(2),2(3),s(4)] with increasing positive entries with sum(s(j)^2,j=1..4) = A004433(n), n >= 1.
%e A223726 a(1) = 1 because  A004433(1) = 30 has only one representation as sum of four distinct nonzero squares, given by the quadruple [1,2,3,4]: 1^2 + 2^2 + 3^2 + 4^2 = 30.
%e A223726 a(16) = 3 because for A004433(3) = 78 the three different quadruples are [1, 2, 3, 8], [1, 4, 5, 6] and [2, 3, 4, 7].
%e A223726 a(48) = 5 because A004433(48) = 126 has five different  representations given by the five quadruples [1, 3, 4, 10], [1, 5, 6, 8], [2, 3, 7, 8], [2, 4, 5, 9], [4, 5, 6, 7].
%Y A223726 Cf. A004433, A025428, A000414, A097203, A222949.
%K A223726 nonn
%O A223726 1,16
%A A223726 _Wolfdieter Lang_, Mar 26 2013