A179015 Number of ways in which n^2 can be expressed as the sum of exactly five positive squares.

0, 0, 0, 1, 1, 1, 2, 5, 2, 6, 6, 9, 9, 15, 8, 25, 20, 21, 25, 39, 26, 46, 44, 57, 49, 71, 52, 102, 81, 81, 99, 145, 92, 156, 126, 164, 160, 204, 151, 247, 217, 236, 245, 326, 211, 357, 319, 381, 360, 416, 344, 518, 446, 476, 450, 670, 468, 675, 607, 661, 668, 825, 625

Offset: 1

Author

Carmine Suriano, Jun 24 2010

Keywords

• nonn

Comments

As n goes to infinity the ratio of a(n)/a(n) of sequence A178898 (using all different squares) tends to 5/4.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..740

Crossrefs

Cf. A000290, A178898.

Cf. A000132. - R. J. Mathar, Jun 26 2010

Cf. A065458, A065459.

Programs

Maple

a(8) = 5 since 64 can be expressed in five different ways as the sum of 5 squares (order is ignored): 8^2 = 7^2+3^2+2^2+1^2+1^2 = 6^2+5^2+1^2+1^2+1^2 = 6^2+4^2+2^2+2^2+2^2 = 6^2+3^2+3^2+3^2+1^2 = 5^2+5^2+3^2+1^2+1^2.

Formula

Asymptotic behavior for large values of n is a(n) = n^2/2-47n/2+243.

a(n) = A025429(n^2). - R. J. Mathar, Jun 26 2010

a(n) = A065459(n) - A065458(n). - Alois P. Heinz, Oct 25 2018