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

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, 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, 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

Offset

1,16

Comments

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.

Links

Table of n, a(n) for n=1..104.

Formula

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.

Example

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.
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].
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].

Crossrefs

Cf. A004433, A025428, A000414, A097203, A222949.

Sequence in context: A030395 A031243 A030394 * A223728 A030596 A031277

Adjacent sequences: A223723 A223724 A223725 * A223727 A223728 A223729

Keyword

nonn

Author

Wolfdieter Lang, Mar 26 2013

Status

approved