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 A216494 G.f. satisfies: A(x) = 1 + x*A(x)^3/(1 - x^4*A(x)^10). 1
 1, 1, 3, 12, 55, 274, 1444, 7923, 44803, 259326, 1529034, 9151733, 55459124, 339595673, 2097962269, 13060078469, 81842038111, 515867610612, 3268440469234, 20803681980270, 132963257157430, 852981624781996, 5490522454007139, 35450567948693263, 229537971398979212, 1490074420399924169, 9696064337840077823 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA G.f. satisfies: A(x) = 1/A(-x*A(x)^5); note that the g.f. of A001764, G(x) = 1 + x*G(x)^3, also satisfies this condition. EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 274*x^5 + 1444*x^6 + 7923*x^7 +... such that A(x) = 1 + x*A(x)^3 + x^5*A(x)^13 + x^9*A(x)^23 + x^13*A(x)^33 + x^17*A(x)^43 +... Given (1) A(x) = 1 + x*A(x)^3 / (1 - x^4*A(x)^10), suppose (2) A(x) = 1/A(-x*A(x)^5), then substituting x in (1) with -x*A(x)^5 yields: 1/A(x) = 1 - x*A(x)^5/A(x)^3 / (1 - x^4*A(x)^20/A(x)^10), which illustrates that (2) is consistent with (1). PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A^3/(1 - x^4*A^10 +x*O(x^n))); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A216493, A001764. Sequence in context: A001764 A171780 A216493 * A120920 A179487 A263533 Adjacent sequences:  A216491 A216492 A216493 * A216495 A216496 A216497 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 07 2012 STATUS approved

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Last modified December 15 20:49 EST 2018. Contains 318154 sequences. (Running on oeis4.)