A159359 Number of n X n arrays of squares of integers summing to 5.

12, 198, 4608, 53730, 378252, 1909236, 7628544, 25628076, 75297420, 198807114, 481029120, 1082267550, 2289691404, 4595197320, 8809614336, 16225724664, 28845544716, 49690719342, 83218759680, 135872231418, 216792905868, 338738351292, 519244496640, 782084374500

Offset

2,1

Comments

As pointed out by Robert Israel in A159355, such arrangments of squares in an n X n array are related to the partitions of the sum (5 in this case). These partitions can be turned into a sum of products of binomial coefficients that computes the desired count, therefore all these sequences have holonomic recurrences. - Georg Fischer, Feb 17 2022

Links

R. H. Hardin, Table of n, a(n) for n = 2..100

Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Formula

Empirical: n^2*(n^2-1)*(n^2+2)*(n^4-11*n^2+48)/120. - R. J. Mathar, Aug 11 2009

Maple

C:=binomial; seq(n^2*(n^2-1)+C(n^2, 5), n=2..22); # Georg Fischer, Feb 17 2022

Crossrefs

Cf. A159355-A159446.

Sequence in context: A048667 A115865 A291285 * A119864 A036240 A346509

Adjacent sequences: A159356 A159357 A159358 * A159360 A159361 A159362

Keyword

nonn,easy

Author

R. H. Hardin, Apr 11 2009

Status

approved