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A240741 Number of compositions of n having exactly six fixed points.

%I A240741 #10 Nov 07 2014 03:44:34
%S A240741 1,1,3,7,16,35,76,155,334,691,1427,2928,5985,12181,24718,50052,101060,
%T A240741 203767,410240,824943,1657225,3326530,6672880,13378262,26809661,
%U A240741 53706442,107555030,215342201,431063039,862743300,1726491928,3454620480,6911903675,13828137410
%N A240741 Number of compositions of n having exactly six fixed points.
%H A240741 Joerg Arndt and Alois P. Heinz, <a href="/A240741/b240741.txt">Table of n, a(n) for n = 21..1000</a>
%F A240741 a(n) ~ c * 2^n, where c = 0.00000076865174785709491795394332754061911033555649913960925841174268897641... . - _Vaclav Kotesovec_, Sep 07 2014
%p A240741 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240741       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 7))
%p A240741     end:
%p A240741 a:= n-> coeff(b(n, 1), x, 6):
%p A240741 seq(a(n), n=21..60);
%t A240741 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, 7}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 6}]; Table[a[n], {n, 21, 60}] (* _Jean-François Alcover_, Nov 07 2014, after Maple *)
%Y A240741 Column k=6 of A238349 and of A238350.
%K A240741 nonn
%O A240741 21,3
%A A240741 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014