cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A235669 Sum of parts of the form 10...0 and 20...0 with nonnegative number of zeros in ternary representation of n as the corresponding numbers 3^n and 2*3^n.

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 6, 3, 4, 9, 4, 5, 4, 3, 4, 7, 4, 5, 18, 7, 8, 5, 4, 5, 8, 5, 6, 27, 10, 11, 6, 5, 6, 9, 6, 7, 10, 5, 6, 5, 4, 5, 8, 5, 6, 19, 8, 9, 6, 5, 6, 9, 6, 7, 54, 19, 20, 9, 8, 9, 12, 9, 10, 11, 6, 7, 6, 5, 6, 9, 6, 7, 20, 9, 10, 7, 6, 7, 10, 7, 8, 81, 28, 29, 12
Offset: 0

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Author

Vladimir Shevelev, Jan 13 2014

Keywords

Comments

The number of appearances of k is the number of compositions of k into numbers of the form 3^n and 2*3^n, A235684(k).

Crossrefs

Programs

  • Mathematica
    bitPatt[n_,b_]:=Split[IntegerDigits[n,b ],#2==0&]; Map[Plus@@Map[FromDigits[#,3]&,bitPatt[#,3]]&,Range[0,50]] (* Peter J. C. Moses, Jan 13 2014 *)

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

Original entry on oeis.org

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

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Author

Keywords

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.
		

Crossrefs

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 *)
Showing 1-2 of 2 results.