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A006429 Number of loopless tree-rooted planar maps with 4 vertices and n faces.
(Formerly M3716)
2
0, 4, 135, 1368, 7350, 28400, 89073, 241220, 585057, 1301420, 2699125, 5282172, 9842430, 17584416, 30289835, 50530680, 81940901, 129557940, 200246795, 303220720, 450674190, 658545360, 947426925, 1343646044, 1880535825, 2599922780, 3553856649, 4806611060 (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.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = n*(n+2)*(13*n^7+268*n^6+2254*n^5+4900*n^4-10703*n^3-62048*n^2+28596*n+137520) / 60480 for n > 1. - Sean A. Irvine, Apr 10 2017
From Chai Wah Wu, Aug 01 2021: (Start)
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 11.
G.f.: x^2*(-5*x^9 + 50*x^8 - 224*x^7 + 590*x^6 - 995*x^5 + 1100*x^4 - 735*x^3 + 198*x^2 + 95*x + 4)/(x - 1)^10. (End)
PROG
(PARI) a(n) = if(n < 2, 0, n*(n+2)*(13*n^7+268*n^6+2254*n^5+4900*n^4-10703*n^3-62048*n^2+28596*n+137520) / 60480) \\ Andrew Howroyd, Apr 03 2021
CROSSREFS
Column 4 of A342985.
Sequence in context: A274703 A045482 A263588 * A016483 A102986 A012160
KEYWORD
nonn
AUTHOR
EXTENSIONS
Title improved by Sean A. Irvine, Apr 10 2017
Terms a(12) and beyond from Andrew Howroyd, Apr 03 2021
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)