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

Author

Geoffrey Critzer, Sep 30 2012

Keywords

• nonn
• easy

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

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

Crossrefs

Row n=3 of A343097.

Cf. A002817 (2 x 2 checkerboard).

Programs

Mathematica

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

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