A261962 Number of compositions of n such that no part equals any of its two immediate predecessors.

1, 1, 1, 3, 3, 5, 11, 15, 23, 37, 67, 101, 165, 265, 419, 691, 1123, 1789, 2909, 4657, 7515, 12183, 19657, 31635, 51101, 82449, 132989, 214623, 346485, 558587, 901399, 1454949, 2347157, 3787197, 6111131, 9858931, 15908393, 25669125, 41416849, 66826277

Offset

0,4

Links

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

Formula

a(n) ~ c * d^n, where d = 1.61350953985228953675390530863679475666564394885974..., c = 0.5270561325668460003703909484716134447490733801644227... - Vaclav Kotesovec, Sep 21 2019

Maple

b:= proc(n, i, j) option remember; `if`(n=0, 1, add(
      `if`(k=i or k=j, 0, (t-> b(t, `if`(k>t, 0, k),
      `if`(i>t, 0, i)))(n-k)), k=1..n))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..50);

Mathematica

b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, Sum[If[k == i || k == j, 0, Function[t, b[t, If[k>t, 0, k], If[i>t, 0, i]]][n - k]], {k, 1, n}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 50] (* Jean-François Alcover, Dec 03 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A261960.

Cf. A261961.

Sequence in context: A279790 A338847 A032020 * A301500 A084656 A073749

Adjacent sequences: A261959 A261960 A261961 * A261963 A261964 A261965

Keyword

nonn

Author

Alois P. Heinz, Sep 06 2015

Status

approved