OFFSET
0,3
COMMENTS
Cycle index of symmetry group (cyclic rotation group of order 4 acting on the 9 cells of the square) is (2s(4)^2*s(1) + s(2)^4*s(1) + s(1)^9)/4.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = n^3*(n^2+1)*(n^4-n^2+2)/4.
G.f.: x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10. - Colin Barker, Feb 23 2017
EXAMPLE
The number of 3 X 3 binary matrices up to rotations is 140.
MATHEMATICA
Table[(2n^3+n^5+n^9)/4, {n, 0, 24}]
PROG
(PARI) concat(0, Vec(x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 19 2017
STATUS
approved