A127680 a(0) = 1; a(n+1) = Sum_{k=0..n} a(n-k)*a(floor(k/2)).

1, 1, 2, 4, 8, 17, 35, 74, 154, 324, 677, 1422, 2977, 6246, 13086, 27444, 57518, 120600, 252794, 529994, 1111013, 2329187, 4882755, 10236280, 21458943, 44986461, 94308415, 197707134, 414469000, 868886834, 1821517772, 3818600772

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x * (1 + x) * A(x^2)). - Ilya Gutkovskiy, Nov 15 2021

a(n) ~ c * d^n, where d = 2.096382783759695271747034891835844892559952962948180418542044889824924... and c = 0.413348184087944400305975399220165744000861336139702047444087822224828... - Vaclav Kotesovec, Nov 16 2021

Mathematica

f[l_List] := Block[{n = Length[l] - 1}, Append[l, Sum[l[[n - k + 1]]*l[[Floor[k/2] + 1]], {k, 0, n}]]]; Nest[f, {1}, 33] (* Ray Chandler, Feb 13 2007 *)

Crossrefs

Cf. A367652, A367653, A367654.

Cf. A127681.

Sequence in context: A001357 A309462 A058520 * A136750 A274115 A097107

Adjacent sequences: A127677 A127678 A127679 * A127681 A127682 A127683

Keyword

easy,nonn

Author

Leroy Quet, Jan 23 2007

Extensions

Extended by Ray Chandler, Feb 13 2007

Status

approved