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 A036437 Triangle of coefficients of generating function of ternary rooted trees of height exactly n. 14
 1, 1, 1, 1, 1, 2, 4, 4, 5, 4, 4, 3, 2, 1, 1, 1, 3, 8, 15, 27, 43, 67, 97, 136, 183, 239, 300, 369, 432, 498, 551, 594, 614, 624, 601, 570, 514, 453, 378, 312, 238, 181, 128, 89, 56, 37, 20, 12, 6, 3, 1, 1, 1, 4, 13, 32, 74, 155, 316, 612, 1160, 2126, 3829, 6737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Alois P. Heinz, Rows n = 1..8, flattened A. T. Balaban, J. W. Kennedy and L. V. Quintas, The number of alkanes having n carbons and a longest chain of length d, J. Chem. Education, 65 (4 (1988), 304-313. Index entries for sequences related to rooted trees FORMULA T_{n}(z) - T_{n-1}(z) (see A036370). EXAMPLE 1; 1, 1, 1; 1, 2, 4, 4, 5, 4, 4, 3, 2, 1, 1; MAPLE df:= (t, l)-> zip((x, y)->x-y, t, l, 0): T:= proc(n) option remember; local f, g; if n=0 then 1 else f:= z-> add([T(n-1)][i]*z^(i-1), i=1..nops([T(n-1)])); g:= expand(1 +z*(f(z)^3/6 +f(z^2)*f(z)/2 +f(z^3)/3)); seq(coeff(g, z, i), i=0..degree(g, z)) fi end: seq(df([T(n)], [T(n-1)])[n+1..-1][], n=1..5); # Alois P. Heinz, Sep 26 2011 MATHEMATICA df[t_, l_] := Plus @@ PadRight[{t, -l}]; T[n_] := T[n] = Module[{f, g}, If[n == 0, {1}, f[z_] := Sum[T[n-1][[i]]*z^(i-1), {i, 1, Length[T[n-1]]}]; g = Expand[1+z*(f[z]^3/6+f[z^2]*f[z]/2+f[z^3]/3)]; Table [Coefficient [g, z, i], {i, 0, Exponent[g, z]}]]]; Table[df[T[n], T[n-1]][[n+1 ;; -1]], {n, 1, 5}] // Flatten (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *) CROSSREFS Sequence in context: A269300 A182215 A036443 * A053306 A108422 A276523 Adjacent sequences: A036434 A036435 A036436 * A036438 A036439 A036440 KEYWORD nonn,easy,tabf AUTHOR N. J. A. Sloane, Eric Rains (rains(AT)caltech.edu) STATUS approved

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Last modified May 30 02:25 EDT 2023. Contains 363044 sequences. (Running on oeis4.)