login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A296508 A299778 A302248 * A089327 A280851 A279391
KEYWORD
nonn,look
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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