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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 (list; graph; refs; listen; history; text; internal format)
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^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

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Last modified May 18 10:28 EDT 2022. Contains 353807 sequences. (Running on oeis4.)