A106357 Number of compositions of n with exactly 1 adjacent equal pair of parts.

1, 0, 3, 6, 7, 20, 42, 72, 141, 280, 516, 976, 1853, 3420, 6361, 11844, 21819, 40192, 73942, 135452, 247828, 452776, 825252, 1501998, 2730159, 4954890, 8981360, 16261568, 29408708, 53130154, 95894384, 172917788, 311538169, 560831286

Offset

2,3

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.

Formula

a(n) ~ c * d^n * n, where d = A241902 = 1.750241291718309031249738624639..., c = 0.04826600476992825168367... . - Vaclav Kotesovec, Sep 05 2014

Maple

b:= proc(n, v) option remember; `if`(n=0, [1, 0],
      add((p-> `if`(i=v, [0, p[1]], p))(b(n-i, i)), i=1..n))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=2..45);  # Alois P. Heinz, May 09 2014

Mathematica

b[n_, v_] := b[n, v] = If[n == 0, {1, 0}, Sum[Function[p, If[i == v, {0, p[[1]]}, p]][b[n - i, i]], {i, 1, n}]];
a[n_] := b[n, 0][[2]];
a /@ Range[2, 45] (* Jean-François Alcover, Nov 02 2020, after Alois P. Heinz *)

Crossrefs

Column 1 of A106356. Cf. A003242.

Cf. A241902.

Sequence in context: A103831 A217519 A364007 * A088101 A050867 A019248

Adjacent sequences: A106354 A106355 A106356 * A106358 A106359 A106360

Keyword

nonn

Author

Christian G. Bower, Apr 29 2005

Extensions

Replaced broken link, Vaclav Kotesovec, May 01 2014

Status

approved