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

%I A240743 #10 Nov 06 2014 09:52:23
%S A240743 1,1,3,7,16,35,76,162,342,706,1474,3030,6207,12660,25739,52174,105516,
%T A240743 212972,429169,863721,1736237,3487091,6998235,14036039,28137051,
%U A240743 56380699,112936022,226157834,452782897,906328973,1813903281,3629837847,7262985540,14531361628
%N A240743 Number of compositions of n having exactly eight fixed points.
%H A240743 Joerg Arndt and Alois P. Heinz, <a href="/A240743/b240743.txt">Table of n, a(n) for n = 36..1000</a>
%F A240743 a(n) ~ c * 2^n, where c = 0.00000000002465665216785151607617323669331409016812218707985200021988733051... . - _Vaclav Kotesovec_, Sep 07 2014
%p A240743 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240743       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 9))
%p A240743     end:
%p A240743 a:= n-> coeff(b(n, 1), x, 8):
%p A240743 seq(a(n), n=36..70);
%t A240743 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 *)
%Y A240743 Column k=8 of A238349 and of A238350.
%K A240743 nonn
%O A240743 36,3
%A A240743 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014