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

Author

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

Keywords

• nonn
• look

Examples

			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.
		

Links

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

Crossrefs

Cf. A235684, A078932, A235669.

Programs

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 *)