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

1, 1, 2, 4, 7, 13, 25, 46, 86, 162, 302, 565, 1058, 1978, 3700, 6923, 12949, 24223, 45316, 84769, 158575, 296645, 554923, 1038079, 1941911, 3632677, 6795551, 12712263, 23780486, 44485521, 83217888, 155673480, 291214232, 544766722, 1019080592, 1906366927

Offset

0,3

Comments

a(n+1)/a(n) tends to 1.87067337504749000600807516613083316430149226... (used Richardson's extrapolation) - Vaclav Kotesovec, Jan 14 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(3) = 4: 1+1+1, 2+1, 1+2, 3, thus we have 4 compositions with the allowed parts.

Maple

a:= proc(n) option remember; `if`(n=0, 1, `if`(n<0, 0,
      add(a(n-3^i)+a(n-2*3^i), i=0..ilog[3](n))))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 13 2014

Mathematica

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]}]]];
a /@ Range[0, 40] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)

Crossrefs

Cf. A078932, A235669, A235773.

Sequence in context: A374517 A079958 A224341 * A367400 A018082 A018083

Adjacent sequences: A235681 A235682 A235683 * A235685 A235686 A235687

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 13 2014

Status

approved