A240738 Number of compositions of n having exactly three fixed points.

1, 1, 3, 7, 12, 30, 61, 126, 258, 537, 1083, 2205, 4465, 9023, 18192, 36612, 73633, 147893, 296818, 595313, 1193351, 2391121, 4789448, 9590503, 19199906, 38430421, 76910470, 153901337, 307932963, 616076971, 1232495756, 2465545205, 4931986957, 9865425657

Offset

6,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) ~ c * 2^n, where c = 0.01795631780689407343024911217251418606332716557572090051127381129853009022... . - Vaclav Kotesovec, Sep 07 2014

Example

a(8) = 3: 1214, 1232, 12311.
a(9) = 7: 1134, 1224, 1233, 12141, 12312, 12321, 123111.
a(10) = 12: 11341, 12115, 12142, 12241, 12313, 12322, 12331, 121411, 123112, 123121, 123211, 1231111.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, series(
      add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 4))
    end:
a:= n-> coeff(b(n, 1), x, 3):
seq(a(n), n=6..45);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Series[Sum[b[n-j, i+1]*If[i == j, x, 1], {j, 1, n}], {x, 0, 4}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 3}]; Table[a[n], {n, 6, 45}] (* Jean-François Alcover, Nov 07 2014, after Maple *)

Crossrefs

Column k=3 of A238349 and of A238350.

Sequence in context: A063072 A007626 A193297 * A047068 A167490 A081533

Adjacent sequences: A240735 A240736 A240737 * A240739 A240740 A240741

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved