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A006565
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Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations.
(Formerly M4942)
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5
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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; internal format)
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OFFSET
| 0,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| n*(n+1)*(n^2+n+1)*(n^2-2*n+2)/6.
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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 S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Cf. A027670, A075195.
Sequence in context: A166794 A038841 A021354 * A206207 A026936 A021114
Adjacent sequences: A006562 A006563 A006564 * A006566 A006567 A006568
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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