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

Author

R. H. Hardin, Apr 11 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A159355-A159446.

Programs

Maple

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

Formula

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