

A159359


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


3



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


FORMULA

Empirical: n^2*(n^21)*(n^2+2)*(n^411*n^2+48)/120.  R. J. Mathar, Aug 11 2009


MAPLE

C:=binomial; seq(n^2*(n^21)+C(n^2, 5), n=2..22); # Georg Fischer, Feb 17 2022


CROSSREFS

Cf. A159355A159446.
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



