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 A352045 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(k). 5
 1, 1, 1, 1, 2, 5, 11, 22, 43, 85, 170, 341, 683, 1367, 2744, 5552, 11381, 23729, 50423, 109220, 240845, 539411, 1223357, 2800535, 6451340, 14915084, 34533851, 79949741, 184865936, 426627122, 982217705, 2255539406, 5166125852, 11802977573, 26903285366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x). E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(3*n) / (3*n)! dx. MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 3 k] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 34}] nmax = 34; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)^3]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] CROSSREFS Cf. A351970, A352044. Sequence in context: A129715 A024493 A130781 * A351970 A071015 A293362 Adjacent sequences: A352042 A352043 A352044 * A352046 A352047 A352048 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 01 2022 STATUS approved

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Last modified March 2 05:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)