A060560 Number of ways to color the vertices of an octagon using <= n colors, allowing rotations and reflections.
0, 1, 30, 498, 4435, 25395, 107331, 365260, 1058058, 2707245, 6278140, 13442286, 26942565, 51084943, 92383305, 160386360, 268718116, 436365945, 689252778, 1062132490, 1600850055, 2365010571, 3431103775, 4896133188, 6881801550, 9539306725, 13054804776, 17655599430
Offset: 0
Keywords
Links
- Harry J. Smith, Table of n, a(n) for n=0..500
- S. G. Williamson, The combinatorial analysis of patterns and the principle of inclusion-exclusion, Discrete Math. 1 (1972), no. 4, 357--388. MR0299493 (45 #8541). - _N. J. A. Sloane_, Mar 27 2012
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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PARI
a(n) = { (n^8 + 4*n^5 + 5*n^4 + 2*n^2 + 4*n)/16 } \\ Harry J. Smith, Jul 07 2009
Formula
a(n) = n*(n + 1)*(n^6 - n^5 + n^4 + 3*n^3 + 2*n^2 - 2*n + 4)/16.
G.f.: x*(1 + 21*x + 264*x^2 + 949*x^3 + 1014*x^4 + 258*x^5 + 13*x^6)/(1 - x)^9. - Colin Barker, Jan 29 2012
Comments