A240742 Number of compositions of n having exactly seven fixed points.

1, 1, 3, 7, 16, 35, 76, 162, 334, 706, 1457, 2996, 6130, 12496, 25383, 51423, 103937, 209723, 422418, 849843, 1707917, 3429407, 6881120, 13798903, 27657921, 55414350, 110989891, 222243203, 444916908, 890536103, 1782217460, 3566301121, 7135641348, 14276228900

Offset

28,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 28..1000

Formula

a(n) ~ c * 2^n, where c = 0.00000000620059990498579334409439332104298331660404026106645127910814204326... . - 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, 8))
    end:
a:= n-> coeff(b(n, 1), x, 7):
seq(a(n), n=28..65);

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, 8}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 7}]; Table[a[n], {n, 28, 65}] (* Jean-François Alcover, Nov 06 2014, after Maple *)

Crossrefs

Column k=7 of A238349 and of A238350.

Sequence in context: A104004 A101509 A240741 * A240743 A240744 A240745

Adjacent sequences: A240739 A240740 A240741 * A240743 A240744 A240745

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved