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

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Column k=3 of A238349 and of A238350.

Programs

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 *)

Formula

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