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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 (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 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

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Last modified May 22 02:24 EDT 2024. Contains 372741 sequences. (Running on oeis4.)