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A051164 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a0,a1,a1,a1,a2,a2,a2,a3,a3,a3,...).

%I A051164 #16 Feb 18 2017 12:18:20
%S A051164 1,2,4,9,21,48,108,243,549,1243,2819,6412,14640,33549,77121,177747,
%T A051164 410565,949992,2200978,5103623,11839783,27471189,63734823,147831594,
%U A051164 342767586,794413545,1840338975,4261443374,9863627962,22822212734,52789053456,122073285984
%N A051164 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a0,a1,a1,a1,a2,a2,a2,a3,a3,a3,...).
%H A051164 Alois P. Heinz, <a href="/A051164/b051164.txt">Table of n, a(n) for n = 0..1000</a>
%H A051164 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A051164 a:= proc(n) option remember; add(`if`(k<3, 1,
%p A051164       a(iquo(k, 3)))*binomial(n, k), k=0..n)
%p A051164     end:
%p A051164 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jul 08 2015
%t A051164 a[n_] := a[n] = Sum[If[k<3, 1, a[Quotient[k, 3]]]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 18 2017, after _Alois P. Heinz_ *)
%Y A051164 Cf. A051163, A051165, A051166.
%K A051164 easy,nonn,eigen
%O A051164 0,2
%A A051164 _Jonas Wallgren_
%E A051164 More terms from _Vladeta Jovovic_, Jul 26 2002