A261984 Number of compositions of n such that the minimal distance between two identical parts equals two.

0, 0, 0, 0, 1, 2, 3, 8, 16, 34, 57, 113, 213, 396, 733, 1333, 2419, 4400, 7934, 14321, 25687, 45947, 82085, 146410, 260547, 463021, 821669, 1456296, 2578051, 4559972, 8057373, 14225124, 25096606, 44246087, 77958821, 137283534, 241626535, 425079358, 747501363

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

a(n) ~ A003242(n). - Vaclav Kotesovec, Sep 08 2015

Example

a(4) = 1: 121.
a(5) = 2: 131, 212.
a(6) = 3: 141, 1212, 2121.
a(7) = 8: 151, 232, 313, 1213, 1312, 2131, 3121, 12121.
a(8) = 16: 161, 242, 323, 1214, 1232, 1313, 1412, 2123, 2141, 2321, 3131, 3212, 4121, 12131, 13121, 21212.

Maple

g:= proc(n, i) option remember; `if`(n=0, 1, add(
     `if`(i=j, 0, g(n-j, j)), j=1..n))
    end:
b:= proc(n, i, m) option remember; `if`(n=0, 0, add(
     `if`(i=j, 0, `if`(j=m, g(n-j, j), b(n-j, j, i))), j=1..n))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..45);

Mathematica

g[n_, i_] := g[n, i] = If[n==0, 1, Sum[If[i==j, 0, g[n-j, j]], {j, 1, n}]];
b[n_, i_, m_] := b[n, i, m] = If[n==0, 0, Sum[If[i==j, 0, If[j==m, g[n-j, j], b[n-j, j, i]]], {j, 1, n}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 45] (* Jean-François Alcover, Dec 21 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A261981.

Sequence in context: A182670 A234696 A169949 * A100321 A324839 A219751

Adjacent sequences: A261981 A261982 A261983 * A261985 A261986 A261987

Keyword

nonn

Author

Alois P. Heinz, Sep 07 2015

Status

approved