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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

%I

%S 1,1,3,12,54,261,1324,6954,37493,206316,1154050,6542485,37507919,

%T 217081155,1266646114,7443100944,44008522719,261631301144,

%U 1562969609155,9377744249277,56486588669929,341452466500382,2070684006442310,12594325039504367,76808163066135791

%N Generating function satisfies A(x)=1-xA(x)+2x(A(x))^2-x^2(A(x))^3+x^2(A(x))^4.

%C Also appears in the context of pattern avoiding ternary trees.

%H Alois P. Heinz, <a href="/A200740/b200740.txt">Table of n, a(n) for n = 0..400</a>

%H Nathan Gabriel, Katherine Peske, Lara Pudwell, and Samuel Tay, <a href="http://arxiv.org/abs/1110.2225">Pattern Avoidance in Ternary Trees</a>, arXiv:1110.2225 [math.CO], 2011.

%H N. Gabriel, K. Peske, L. Pudwell, S. Tay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Pudwell/pudwell.html">Pattern Avoidance in Ternary Trees</a>, J. Int. Seq. 15 (2012) # 12.1.5.

%p n:=30:

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

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

%p Y:=expand(L):

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

%p p[i]:=coeff(Y,x,i):

%p od:

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

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

%p # second Maple program:

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

%p , x, n+1), x, n):

%p seq(a(n), n=0..40); # _Alois P. Heinz_, Nov 09 2013

%t 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 *)

%K nonn

%O 0,3

%A _Lara Pudwell_, Nov 21 2011

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Last modified August 5 20:11 EDT 2021. Contains 346488 sequences. (Running on oeis4.)