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A159359
Number of n X n arrays of squares of integers summing to 5.
19
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
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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Apr 11 2009
STATUS
approved