OFFSET
0,5
COMMENTS
Computed using Polya's enumeration theorem for coloring.
LINKS
María Merino, Table of n, a(n) for n = 0..29
M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).
FORMULA
G.f.: g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) = (1/8)*(y1^(n^2)+2*y1^n*y2^((n^2-n)/2)+3*y2^(n^2/2)+2*y4^(n^2/4)) if n even and (1/8)*(y1^(n^2)+4*y1^n*y2^((n^2-n)/2)+y1*y2^((n^2-1)/2)+2*y1*y4^((n^2-1)/4)) if n odd, where coefficient correspond to y1=Sum_{i=1..10} x_i, y2=Sum_{i=1..10} x_i^2, y4=Sum_{i=1..10} x_i^4 and occurrences of numbers are ceiling(n^2/10) for the first k numbers and floor(n^2/10) for the last (10-k) numbers, if n^2 = k mod 10.
EXAMPLE
For n = 3 the a(4) = 40864828320 solutions are colorings of 4 X 4 matrices in 10 colors inequivalent under the action of D_4 with exactly occurrences 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 of each color (coefficient of x1^2 x2^2 x3^2 x4^2 x5^2 x6^2 x7^1 x8^1 x9^1 x10^1).
CROSSREFS
KEYWORD
nonn
AUTHOR
María Merino, Imanol Unanue, May 22 2017
STATUS
approved