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 A036651 Number of centered 6-valent trees with n nodes. 3
 0, 1, 0, 1, 1, 2, 3, 7, 11, 26, 52, 120, 266, 640, 1509, 3702, 9090, 22781, 57452, 146783, 377357, 978342, 2550611, 6690242, 17633855, 46705333, 124227015, 331757697, 889207207, 2391478247, 6451880415, 17457214729, 47363110968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees)., J. Integer Sequences, Vol. 2 (1999), Article 99.1.1. MATHEMATICA n = 20; (* algorithm from Rains and Sloane *) S5[f_, h_, x_] := f[h, x]^5/120 + f[h, x]^3 f[h, x^2]/12 + f[h, x]^2 f[h, x^3]/6 + f[h, x] f[h, x^2]^2/8 + f[h, x] f[h, x^4]/4 + f[h, x^2] f[h, x^3]/6 + f[h, x^5]/5; S6[f_, h_, x_] := f[h, x]^6/720 + f[h, x]^4 f[h, x^2]/48 + f[h, x]^3 f[h, x^3]/18 + f[h, x]^2 f[h, x^2]^2/16 + f[h, x]^2 f[h, x^4]/8 + f[h, x] f[h, x^2] f[h, x^3]/6 + f[h, x] f[h, x^5]/5 + f[h, x^2]^3/48 + f[h, x^2] f[h, x^4]/8 + f[h, x^3]^2/18 + f[h, x^6]/6; T[-1, z_] := 1;  T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S5[T, h-1, z]z, z], n+1]; Sum[Take[CoefficientList[z^(n+1) + S6[T, h-1, z]z - S6[T, h-2, z]z - (T[h-1, z] - T[h-2, z]) (T[h-1, z]-1), z], n+1], {h, 1, n/2}] + PadRight[{0, 1}, n+1] (* Robert A. Russell, Sep 15 2018 *) CROSSREFS A036651 = A036653 - A036652. Sequence in context: A005246 A116406 A112843 * A049454 A095055 A305750 Adjacent sequences:  A036648 A036649 A036650 * A036652 A036653 A036654 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)