login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 1 09:36 EDT 2021. Contains 346385 sequences. (Running on oeis4.)