A178898 a(n) = number of ways in which n^2 can be expressed as the sum of five different squares.

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, 43, 43, 60, 51, 66, 61, 88, 83, 105, 91, 137, 116, 124, 140, 185, 143, 195, 187, 233, 197, 266, 220, 317, 283, 318, 317, 371, 331, 433, 404, 476, 450, 529, 427, 620, 543, 616

Offset

1,15

Comments

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.

Links

Table of n, a(n) for n=1..66.

Formula

a(n) = A025444(n^2). [From R. J. Mathar, Oct 18 2010]

Example

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.

Crossrefs

Sequence in context: A371590 A048680 A342793 * A296616 A143529 A331010

Adjacent sequences: A178895 A178896 A178897 * A178899 A178900 A178901

Keyword

nonn

Author

Carmine Suriano, Jun 21 2010

Status

approved