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

Author

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

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A078932, A235669, A235773.

Programs

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 *)