A006565 Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations. (Formerly M4942)

0, 1, 14, 130, 700, 2635, 7826, 19684, 43800, 88725, 166870, 295526, 498004, 804895, 1255450, 1899080, 2796976, 4023849, 5669790, 7842250, 10668140, 14296051, 18898594, 24674860, 31853000, 40692925, 51489126, 64573614

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..27.

Victor Meally, Letter to N. J. A. Sloane, no date.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Formula

n*(n+1)*(n^2+n+1)*(n^2-2*n+2)/6.

Maple

A006565 := n-> (n^6+n^3+2*n^2+2*n)/6.
A006565:=-(1+7*z+53*z**2+49*z**3+10*z**4)/(z-1)**7; [Conjectured by Simon Plouffe in his 1992 dissertation.]

Crossrefs

Cf. A027670, A075195.

Sequence in context: A240189 A021354 A208427 * A206207 A358168 A026936

Adjacent sequences: A006562 A006563 A006564 * A006566 A006567 A006568

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved