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A006565 Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations.
(Formerly M4942)
7
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 (list; graph; refs; listen; history; text; internal format)
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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 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 A026936 A021114

Adjacent sequences:  A006562 A006563 A006564 * A006566 A006567 A006568

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)