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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 Andrew Howroyd, Table of n, a(n) for n = 1..1000 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 Adjacent sequences: A006426 A006427 A006428 * A006430 A006431 A006432 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 December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)