A036374 Number of ternary rooted trees with n nodes and height at most 6.

1, 1, 1, 2, 4, 8, 17, 38, 82, 177, 376, 789, 1638, 3376, 6894, 13987, 28181, 56424, 112282, 222171, 437098, 855311, 1664755, 3223402, 6209505, 11901967, 22700056, 43083657, 81376732, 152971812, 286199220, 532954482, 987861697, 1822655134

Offset

0,4

Links

Sean A. Irvine, Table of n, a(n) for n = 0..364

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 rooted trees

Formula

If T_i(z) = g.f. for ternary trees of height at most i, T_{i+1}(z)=1+z*(T_i(z)^3/6+T_i(z^2)*T_i(z)/2+T_i(z^3)/3); T_0(z) = 1.

Mathematica

T[0] = {1}; T[n_] := T[n] = Module[{f, g}, f[z_] := Sum[T[n - 1][[i]]*z^(i - 1), {i, 1, Length[T[n - 1]]}]; g = 1 + z*(f[z]^3/6 + f[z^2]*f[z]/2 + f[z^3]/3); CoefficientList[g, z]]; A036374 = T[6] (* Jean-François Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

Crossrefs

Cf. A036370.

Sequence in context: A179476 A087803 A212658 * A214999 A348756 A348755

Adjacent sequences: A036371 A036372 A036373 * A036375 A036376 A036377

Keyword

nonn,fini,full

Author

N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)

Status

approved