A036652 Number of bicentered 6-valent trees with n nodes.

0, 0, 1, 0, 1, 1, 3, 4, 11, 19, 49, 103, 254, 583, 1445, 3506, 8815, 22082, 56286, 143822, 371354, 963250, 2516822, 6607348, 17440933, 46233833, 123090070, 328923702, 882114742, 2373351473, 6405275496, 17336081498, 47047112028

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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.
• Index entries for sequences related to trees

Crossrefs

Cf. A036651, A036653.

Programs

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;
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) + (T[h,z] - T[h-1,z])^2/2 + (T[h,z^2] - T[h-1,z^2])/2, z],n+1], {h,0,n/2}] (* Robert A. Russell, Sep 15 2018 *)

Formula

a(n) = A036653(n) - A036651(n).