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A006428 Number of loopless tree-rooted planar maps with 3 vertices and n faces and no isthmuses.
(Formerly M3139)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
FORMULA
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
The above conjectures are true. - Andrew Howroyd, Apr 03 2021
From Chai Wah Wu, Aug 08 2022: (Start)
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)
PROG
(PARI) a(n) = if(n<2, 0, n*(n+1)*(n^3+6*n^2+11*n-42) / 24) \\ Andrew Howroyd, Apr 03 2021
CROSSREFS
Column 3 of A342985.
Sequence in context: A268591 A275560 A213848 * A068619 A247768 A168075
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Title improved by Sean A. Irvine, Apr 10 2017
Terms a(13) and beyond from Andrew Howroyd, Apr 03 2021
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)