A036648 - OEIS

A036648

Number of centered 5-valent trees with n nodes.

0, 1, 0, 1, 1, 2, 3, 6, 11, 24, 48, 109, 242, 574, 1346, 3258, 7928, 19664, 49158, 124384, 316791, 813231, 2099326, 5451613, 14226697, 37306971, 98247737, 259779698, 689385447, 1835644498, 4902992215, 13133825317, 35276818036

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..32.

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.

Index entries for sequences related to trees

FORMULA

a(n) = A036650(n) - A036649(n).

MATHEMATICA

n = 30; (* algorithm from Rains and Sloane *)

S4[f_, h_, x_] := f[h, x]^4/24 + f[h, x]^2 f[h, x^2]/4 + f[h, x] f[h, x^3]/3 + f[h, x^2]^2/8 + f[h, x^4]/4;

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;

T[-1, z_] := 1; T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S4[T, h-1, z]z, z], n+1];

Sum[Take[CoefficientList[z^(n+1) + S5[T, h-1, z]z - S5[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

Cf. A036649, A036650.

Sequence in context: A006787 A176425 A000992 * A047750 A072187 A072374

Adjacent sequences: A036645 A036646 A036647 * A036649 A036650 A036651

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved