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

1,7

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

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

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.

Crossrefs

Cf. A000290, A178898.

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

Cf. A065458, A065459.

Sequence in context: A198539 A121311 A242403 * A195621 A267090 A067948

Adjacent sequences: A179012 A179013 A179014 * A179016 A179017 A179018

Keyword

nonn

Author

Carmine Suriano, Jun 24 2010

Status

approved