A240740 Number of compositions of n having exactly five fixed points.

1, 1, 3, 7, 16, 35, 70, 155, 321, 665, 1368, 2802, 5711, 11623, 23526, 47567, 95967, 193316, 388893, 781519, 1569154, 3148292, 6313052, 12652917, 25349663, 50770869, 101658425, 203506976, 407323589, 815151106, 1631122032, 3263576647, 6529319168, 13062156519

Offset

15,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 15..1000

Formula

a(n) ~ c * 2^n, where c = 0.00004645976701216392005148703795279235922588728788878226802174676992574918... . - Vaclav Kotesovec, Sep 07 2014

Example

a(17) = 3: 123416, 123452, 1234511.
a(18) = 7: 123156, 123426, 123453, 1234161, 1234512, 1234521, 12345111.
a(19) = 16: 121456, 123256, 123436, 123454, 1231561, 1234117, 1234162, 1234261, 1234513, 1234522, 1234531, 12341611, 12345112, 12345121, 12345211, 123451111.

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, 6))
    end:
a:= n-> coeff(b(n, 1), x, 5):
seq(a(n), n=15..50);

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, 6}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 5}]; Table[a[n], {n, 15, 50}] (* Jean-François Alcover, Nov 07 2014, after Maple *)

Crossrefs

Column k=5 of A238349 and of A238350.

Sequence in context: A335713 A026734 A026767 * A239257 A268394 A238913

Adjacent sequences: A240737 A240738 A240739 * A240741 A240742 A240743

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved