A240743 Number of compositions of n having exactly eight fixed points.

1, 1, 3, 7, 16, 35, 76, 162, 342, 706, 1474, 3030, 6207, 12660, 25739, 52174, 105516, 212972, 429169, 863721, 1736237, 3487091, 6998235, 14036039, 28137051, 56380699, 112936022, 226157834, 452782897, 906328973, 1813903281, 3629837847, 7262985540, 14531361628

Offset

36,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 36..1000

Formula

a(n) ~ c * 2^n, where c = 0.00000000002465665216785151607617323669331409016812218707985200021988733051... . - 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, 9))
    end:
a:= n-> coeff(b(n, 1), x, 8):
seq(a(n), n=36..70);

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, 9}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 8}]; Table[a[n], {n, 36, 70}] (* Jean-François Alcover, Nov 06 2014, after Maple *)

Crossrefs

Column k=8 of A238349 and of A238350.

Sequence in context: A101509 A240741 A240742 * A240744 A240745 A227682

Adjacent sequences: A240740 A240741 A240742 * A240744 A240745 A240746

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 11 2014

Status

approved