A235773 Number of compositions of n into distinct powers of 3 and doubled powers of 3.

1, 1, 1, 3, 2, 2, 7, 2, 2, 9, 8, 8, 32, 6, 6, 26, 6, 6, 31, 26, 26, 128, 6, 6, 26, 6, 6, 33, 32, 32, 158, 30, 30, 152, 30, 30, 176, 150, 150, 870, 24, 24, 126, 24, 24, 146, 126, 126, 750, 24, 24, 126, 24, 24, 151, 146, 146, 872, 126, 126, 770, 126, 126, 872

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

Let n=5. We have only two allowed compositions 2+3 = 3+2. So a(5) = 2.
For n=6, we have compositions 6 = 1+2+3 = 1+3+2 = 2+3+1 = 2+1+3 = 3+2+1 = 3+1+2. Thus a(6) = 7.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
      expand(b(n, i-1)+`if`(3*3^i>n, 0, b(n-3*3^i, i-1)*x^2)
      +add(`if`(j*3^i>n, 0, b(n-j*3^i, i-1))*x, j=1..2))))
    end:
a:= n->(p->add(coeff(p, x, j)*j!, j=0..degree(p)))(b(n, ilog[3](n))):
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 15 2014

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<0, 0, Expand[b[n, i-1] + If[3^(i+1) > n, 0, b[n-3^(i+1), i-1]x^2] + Sum[If[3^i j > n, 0, b[n-3^i j, i-1]]x, {j, 1, 2}]]]];
a[n_] := With[{p = b[n, Log[3, n] // Floor]}, Sum[Coefficient[p, x, j] j!, {j, 0, Exponent[p, x]}]];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 12 2020, after Alois P. Heinz *)

Crossrefs

Cf. A235684, A078932, A235669.

Sequence in context: A296508 A299778 A302248 * A089327 A280851 A279391

Adjacent sequences: A235770 A235771 A235772 * A235774 A235775 A235776

Keyword

nonn,look

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 15 2014

Status

approved