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A200740
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Generating function satisfies A(x)=1-xA(x)+2x(A(x))^2-x^2(A(x))^3+x^2(A(x))^4.
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1
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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
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OFFSET
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0,3
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COMMENTS
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Also appears in the context of pattern avoiding ternary trees.
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LINKS
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FORMULA
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D-finite with recurrence 9*n*(3*n+2)*(9637049385113*n -13150529182719) *(3*n+1)*a(n) +3*(-1867245272511941*n^4 +3938815702450522*n^3 -1829703422934531*n^2 -40908425929938*n +80119802734368)*a(n-1) +3*(1493812832168185*n^4 -11081290962331766*n^3 +30368478809400583*n^2 -37445753408742482*n +17518049080170408)*a(n-2) +2*(-3598515629532857*n^4 +51918859363655934*n^3 -272767116207263419*n^2 +607523860755165342*n -484618766805936168)*a(n-3) +2*(2236067158786314*n^4 -43895348429968415*n^3 +313117370004358791*n^2 -968797762596343960*n +1100409843957627312)*a(n-4) +4*(-320929802901755*n^4 +7262334358284366*n^3 -58466924652690997*n^2 +201695420809801662*n -253987363669614120)*a(n-5) +2*(n-6) *(56449675289272*n^3 -1539119961654835*n^2 +11344967150541329*n -25343984173596980)*a(n-6) +2*(n-6) *(n-7) *(88750351258118*n^2 -884530270439421*n +2059300905886804)*a(n-7) +4*-(6920632454763*n -35058029508284)*(n-7)*(n-8)*(2*n-15)*a(n-8)=0. - R. J. Mathar, Jan 11 2024
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MAPLE
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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):
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MATHEMATICA
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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-François Alcover, Nov 28 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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