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A276285 Number of ways of writing n as a sum of 13 squares. 6
1, 26, 312, 2288, 11466, 41808, 116688, 265408, 535704, 1031914, 1899664, 3214224, 5043376, 7801744, 12066912, 17689152, 24443978, 34039200, 48210760, 64966096, 83323344, 109157152, 145532816, 185245632, 227110416, 284788010, 363737712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

More generally, the ordinary generating function for the number of ways of writing n as a sum of k squares is theta_3(0, q)^k = 1 + 2*k*q + 2*(k - 1)*k*q^2 + (4/3)*(k - 2)*(k - 1)*k*q^3 + (2/3)*((k - 3)*(k - 2)*(k - 1) + 3)*k*q^4 + (4/15) *(k - 1)*k*(k^3 - 9*k^2 + 26*k - 9)*q^5 + ..., where theta is the Jacobi theta functions.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Sum of Squares Function

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

FORMULA

G.f.: theta_3(0,q)^13, where theta_3(x,q) is the third Jacobi theta function.

a(n) = (26/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - Seiichi Manyama, May 27 2017

MATHEMATICA

Table[SquaresR[13, n], {n, 0, 26}]

CROSSREFS

13th column of A286815. - Seiichi Manyama, May 27 2017

Row d=13 of A122141.

Cf. Number of ways of writing n as a sum of k squares: A004018 (k = 2), A005875 (k = 3), A000118 (k = 4), A000132 (k = 5), A000141 (k = 6), A008451 (k = 7), A000143 (k = 8), A008452 (k = 9), A000144 (k = 10), A008453 (k = 11), A000145 (k = 12), this sequence (k = 13), A000152 (k = 16).

Sequence in context: A000498 A066912 A015800 * A232064 A030647 A202292

Adjacent sequences:  A276282 A276283 A276284 * A276286 A276287 A276288

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Aug 27 2016

STATUS

approved

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Last modified October 19 20:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)