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 A072493 a(1)=1, a(n) = ceiling((Sum_{k=1..n-1} a(k))/3). 82

%I

%S 1,1,1,1,2,2,3,4,5,7,9,12,16,22,29,39,52,69,92,123,164,218,291,388,

%T 517,690,920,1226,1635,2180,2907,3876,5168,6890,9187,12249,16332,

%U 21776,29035,38713,51618,68824,91765,122353,163138,217517,290023,386697

%N a(1)=1, a(n) = ceiling((Sum_{k=1..n-1} a(k))/3).

%C Is this sequence, with its first 8 terms removed, the same as A005427? See also the similar conjecture with A005428/A073941. - _Ralf Stephan_, Apr 04 2003

%C Yes; the first 8 terms sum to 15, so upon dividing by 3 they are equivalent to the +5 in the formula for A005427. - _Charlie Neder_, Jan 10 2019

%H Michel Marcus, <a href="/A072493/b072493.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling(c*(4/3)^n-1/2) where c=0.389324199524937508840138455...

%t f[s_] := Append[s, Ceiling[Plus @@ s/3]]; Nest[f, {1}, 52] (* _Robert G. Wilson v_, Jul 07 2006 *)

%o (PARI) lista(nn) = {va = vector(nn); va = 1; for (n=2, nn, va[n] = ceil(sum(k=1, n-1, va[k])/3);); va;} \\ _Michel Marcus_, Apr 16 2015

%Y Cf. A073941, A005427, A005428.

%K nonn

%O 1,5

%A _Benoit Cloitre_, Nov 22 2002

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Last modified July 10 16:22 EDT 2020. Contains 335577 sequences. (Running on oeis4.)