cp's OEIS Frontend

A235684 Number of compositions of n into powers of 3 and doubled powers of 3.

%I A235684 #26 Nov 07 2020 09:42:16
%S A235684 1,1,2,4,7,13,25,46,86,162,302,565,1058,1978,3700,6923,12949,24223,
%T A235684 45316,84769,158575,296645,554923,1038079,1941911,3632677,6795551,
%U A235684 12712263,23780486,44485521,83217888,155673480,291214232,544766722,1019080592,1906366927
%N A235684 Number of compositions of n into powers of 3 and doubled powers of 3.
%C A235684 a(n+1)/a(n) tends to 1.87067337504749000600807516613083316430149226... (used Richardson's extrapolation) - _Vaclav Kotesovec_, Jan 14 2014
%H A235684 Alois P. Heinz, <a href="/A235684/b235684.txt">Table of n, a(n) for n = 0..1000</a>
%e A235684 a(3) = 4: 1+1+1, 2+1, 1+2, 3, thus we have 4 compositions with the allowed parts.
%p A235684 a:= proc(n) option remember; `if`(n=0, 1, `if`(n<0, 0,
%p A235684       add(a(n-3^i)+a(n-2*3^i), i=0..ilog[3](n))))
%p A235684     end:
%p A235684 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jan 13 2014
%t A235684 a[n_] := a[n] = If[n == 0, 1, If[n < 0, 0, Sum[a[n - 3^i] + a[n - 2*3^i], {i, 0, Log[3, n]}]]];
%t A235684 a /@ Range[0, 40] (* _Jean-François Alcover_, Nov 07 2020, after _Alois P. Heinz_ *)
%Y A235684 Cf. A078932, A235669, A235773.
%K A235684 nonn
%O A235684 0,3
%A A235684 _Vladimir Shevelev_ and _Peter J. C. Moses_, Jan 13 2014