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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
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
Sequence in context: A048667 A115865 A291285 * A119864 A036240 A346509
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.)