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A004127
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Number of planar hexagon trees with n hexagons.
(Formerly M2936)
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3
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1, 1, 3, 12, 68, 483, 3946, 34485, 315810, 2984570, 28907970, 285601251, 2868869733, 29227904840, 301430074416, 3141985563575, 33059739636198, 350763452126835, 3749420616902637, 40348040718155170, 436827335493148600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| L. W. Beineke and R. E. Pippert, On the enumeration of planar trees of hexagons, Glasgow Math. J., 15 (1974), 131-147.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to trees
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FORMULA
| See Theorem 3 on p. 142 in the Beineke-Pippert paper; also the Maple and Mathematica codes here.
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MAPLE
| T := proc(n) if floor(n)=n then binomial(5*n+1, n)/(5*n+1) else 0 fi end: U := proc(n) if n mod 2 = 0 then binomial(5*n/2+1, n/2)/(5*n/2+1) else 6*binomial((5*n+1)/2, (n-1)/2)/(5*n+1) fi end: S := n->T(n)/4/(2*n+1)+T(n/2)/6+(5*n-2)*T((n-1)/3)/6/(2*n+1)+T((n-1)/6)/6+7*U(n)/12: seq(S(n), n=1..25); (Emeric Deutsch)
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MATHEMATICA
| p=6; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)], 3Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1, 2}]])/2, {n, 1, 20}] - Robert A. Russell (russell(AT)post.harvard.edu), Dec 11 2004
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CROSSREFS
| Cf. A005419, A005040, A002294.
Sequence in context: A187118 A121812 A039750 * A058115 A101313 A144008
Adjacent sequences: A004124 A004125 A004126 * A004128 A004129 A004130
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 22 2004
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