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 A235773 Number of compositions of n into distinct powers of 3 and doubled powers of 3. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 21 13:52 EST 2024. Contains 370235 sequences. (Running on oeis4.)