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A036374 Number of ternary rooted trees with n nodes and height at most 6. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..33.

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-Fran├žois Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

CROSSREFS

Cf. A036370.

Sequence in context: A179476 A087803 A212658 * A214999 A084635 A294529

Adjacent sequences:  A036371 A036372 A036373 * A036375 A036376 A036377

KEYWORD

nonn,fini

AUTHOR

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

STATUS

approved

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Last modified February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)