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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Apr 11 2009
STATUS
approved