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A023422
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Generalized Catalan Numbers.
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5
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1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 129, 261, 530, 1080, 2208, 4528, 9313, 19207, 39714, 82314, 170996, 355976, 742545, 1551817, 3248823, 6812947, 14309557, 30099645, 63402315
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history;
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OFFSET
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0,7
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..2926
A. Goupil, M.-E. Pellerin and J. de Wouters d'oplinter, Snake Polyominoes, arXiv preprint arXiv:1307.8432, 2013. (Gives a g.f.)
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FORMULA
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G.f. A(x) satisfies: A(x) = (1 + x^2 * A(x)^2) / (1 - x + x^2 + x^3 + x^4 + x^5). - Ilya Gutkovskiy, Jul 20 2021
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MATHEMATICA
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a[0]=1; a[n_]:= a[n]=a[n-1] + Sum[a[k]*a[n-2-k], {k, 4, n-2}]; Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Jan 01 2018 *)
B[q_] = (q^2 + q^3 + q^4 + q^5 - Sqrt[((q(q^5 - 1))/(q - 1) - 1)^2 - 4q^6] - q + 1)/(2q^2); CoefficientList[B[q] + O[q]^31, q] (* Jean-François Alcover, Jan 29 2019 *)
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PROG
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(PARI) {a(n) = if(n==0, 1, a(n-1) + sum(k=4, n-2, a(k)*a(n-k-2)))};
for(n=0, 30, print1(a(n), ", ")) \\ G. C. Greubel, Jan 01 2018
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CROSSREFS
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Cf. A000108, A001006, A004148, A004149, A023421, A023423.
Fifth row of A064645.
Sequence in context: A278995 A117302 A265407 * A084638 A157021 A210543
Adjacent sequences: A023419 A023420 A023421 * A023423 A023424 A023425
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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