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A127681 a(0) = 1. a(n+1) = sum{k=0 to n} a(n-k)*a(ceiling(k/2)). 2
1, 1, 2, 4, 9, 19, 42, 90, 198, 428, 936, 2030, 4430, 9626, 20978, 45622, 99367, 216197, 470736, 1024420, 2230183, 4853881, 10566170, 22997974, 50061240, 108964596, 237186018, 516272178, 1123772192, 2446081048, 5324371354, 11589437278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..2958

FORMULA

a(n) ~ c * d^n, where d = 2.17668434612191638687360948440303534082431658053308188275404767951385648... and c = 0.39120452795484998747876543545867360129596245925827624710922741574667... - Vaclav Kotesovec, Nov 16 2021

MAPLE

f:= proc(n) option remember;

add(procname(n-1-k)*procname(ceil(k/2)), k=0..n-1)

end proc:

f(0):= 1:

map(f, [$0..40]); # Robert Israel, Feb 16 2018

MATHEMATICA

f[l_List] := Block[{n = Length[l] - 1}, Append[l, Sum[l[[n - k + 1]]*l[[Ceiling[k/2] + 1]], {k, 0, n}]]]; Nest[f, {1}, 32] (* Ray Chandler, Feb 13 2007 *)

CROSSREFS

Cf. A127680.

Sequence in context: A001384 A089941 A307464 * A192923 A192673 A193021

Adjacent sequences: A127678 A127679 A127680 * A127682 A127683 A127684

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, Jan 23 2007

EXTENSIONS

Extended by Ray Chandler, Feb 13 2007

STATUS

approved

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Last modified November 27 22:56 EST 2022. Contains 358406 sequences. (Running on oeis4.)