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A006428
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Number of loopless tree-rooted planar maps with 3 vertices and n faces and no isthmuses.
(Formerly M3139)
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2
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0, 3, 36, 135, 360, 798, 1568, 2826, 4770, 7645, 11748, 17433, 25116, 35280, 48480, 65348, 86598, 113031, 145540, 185115, 232848, 289938, 357696, 437550, 531050, 639873, 765828, 910861, 1077060, 1266660, 1482048, 1725768, 2000526, 2309195, 2654820, 3040623
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) seems to be divisible by n+1. - Ralf Stephan, Sep 01 2003
Conjecture (for n > 1): a(n) = n*(n+1)*(n^3+6*n^2+11*n-42) / 24. - Sean A. Irvine, Apr 10 2017
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 7.
G.f.: x^2*(2*x^5 - 12*x^4 + 30*x^3 - 36*x^2 + 18*x + 3)/(x - 1)^6. (End)
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PROG
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(PARI) a(n) = if(n<2, 0, n*(n+1)*(n^3+6*n^2+11*n-42) / 24) \\ Andrew Howroyd, Apr 03 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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