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A200740 Generating function satisfies A(x)=1-xA(x)+2x(A(x))^2-x^2(A(x))^3+x^2(A(x))^4. 1
1, 1, 3, 12, 54, 261, 1324, 6954, 37493, 206316, 1154050, 6542485, 37507919, 217081155, 1266646114, 7443100944, 44008522719, 261631301144, 1562969609155, 9377744249277, 56486588669929, 341452466500382, 2070684006442310, 12594325039504367, 76808163066135791 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also appears in the context of pattern avoiding ternary trees.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

Nathan Gabriel, Katherine Peske, Lara Pudwell, and Samuel Tay, Pattern Avoidance in Ternary Trees, arXiv:1110.2225 [math.CO], 2011.

N. Gabriel, K. Peske, L. Pudwell, S. Tay, Pattern Avoidance in Ternary Trees, J. Int. Seq. 15 (2012) # 12.1.5.

MAPLE

n:=30:

L:=1 - a - x*a + 2*x*a^2 - x^2*a^3 + x^2*a^4:

L:=subs(a=add(q[k]*x^k, k=0..n), L):

Y:=expand(L):

for i from 0 to degree(Y, x) do

    p[i]:=coeff(Y, x, i):

od:

S:=solve({ seq(p[t]=0, t=0..n)}, {seq(q[t], t=0..n)}):

normal(subs(S, [seq(q[t], t=0..n)]));

# second Maple program:

a:= n-> coeff(series(RootOf(A=1-x*A+2*x*A^2-x^2*A^3+x^2*A^4, A)

        , x, n+1), x, n):

seq(a(n), n=0..40);  # Alois P. Heinz, Nov 09 2013

MATHEMATICA

A[_] = 0; Do[A[x_] = 1 - x A[x] + 2x A[x]^2 - x^2 A[x]^3 + x^2 A[x]^4 + O[x]^25, {25}]; CoefficientList[A[x], x] (* Jean-Fran├žois Alcover, Nov 28 2018 *)

CROSSREFS

Sequence in context: A006026 A158826 A107264 * A177133 A186241 A193115

Adjacent sequences:  A200737 A200738 A200739 * A200741 A200742 A200743

KEYWORD

nonn

AUTHOR

Lara Pudwell, Nov 21 2011

STATUS

approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)