A240744 Number of compositions of n having exactly nine fixed points.

1, 1, 3, 7, 16, 35, 76, 162, 342, 715, 1474, 3049, 6245, 12746, 25922, 52571, 106353, 214731, 432827, 871240, 1751725, 3518787, 7062725, 14167004, 28402284, 56916681, 114017164, 228335406, 457163368, 915131854, 1831578490, 3665302380, 7334102844, 14673905376

Offset

45,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 45..1000

Formula

a(n) ~ c * 2^n, where c = 0.00000000000004863374631933235641619389991611011374568106537836728124272498... . - Vaclav Kotesovec, Sep 07 2014

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, 10))
    end:
a:= n-> coeff(b(n, 1), x, 9):
seq(a(n), n=45..80);

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, 10}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 9}]; Table[a[n], {n, 45, 80}] (* Jean-François Alcover, Nov 06 2014, after Maple *)

Crossrefs

Column k=9 of A238349 and of A238350.

Sequence in context: A240741 A240742 A240743 * A240745 A227682 A099325

Adjacent sequences: A240741 A240742 A240743 * A240745 A240746 A240747

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved