

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^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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



