A217331 Number of inequivalent ways to color a 3 X 3 checkerboard using at most n colors allowing rotations and reflections.

0, 1, 102, 2862, 34960, 252375, 1284066, 5105212, 16912512, 48700845, 125512750, 295649706, 646497072, 1328022787, 2586463530, 4811211000, 8598455296, 14835732057, 24812155062, 40359796390, 64032402000

Offset

0,3

Comments

Cycle index of symmetry group is (s(1)^9 + s(1)*s(2)^4 + 2*s(1)*s(4)^2 + 4*s(1)^3*s(2)^3)/8.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = (n^9 + n^5 + 2*n^3 + 4*n^6)/8.

G.f.: x*(38*x^7+1753*x^6+11244*x^5+19535*x^4+10810*x^3+1887*x^2+92*x+1)/(x-1)^10. - Colin Barker, Oct 04 2012

Mathematica

Table[(n^9+n^5+2*n^3+4*n^6)/8, {n, 0, 20}]

Crossrefs

Row n=3 of A343097.

Cf. A002817 (2 x 2 checkerboard).

Sequence in context: A223308 A230737 A203401 * A284448 A274252 A303993

Adjacent sequences: A217328 A217329 A217330 * A217332 A217333 A217334

Keyword

nonn,easy

Author

Geoffrey Critzer, Sep 30 2012

Status

approved