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%I #17 Nov 03 2016 11:10:50
%S 1,1,1,2,3,5,8,13,22,36,61,101,169,283,473,793,1325,2220,3715,6220,
%T 10413,17431,29185,48856,81797,136937,229257,383813,642564,1075762,
%U 1800995,3015171,5047886,8451001,14148368,23686705,39655467,66389797,111147511,186079299,311527531,521548600
%N G.f.: 1/(1 - x*(1-x^5)/(1 - x^2*(1-x^6)/(1 - x^3*(1-x^7)/(1 - x^4*(1-x^8)/(1 - x^5*(1-x^9)/(1 - ...)))))), a continued fraction.
%C Limit a(n)/a(n+1) = 0.597312551712707899432116871133154503665320273329853...
%H Alois P. Heinz, <a href="/A227374/b227374.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: T(0), where T(k) = 1 - x^(k+1)*(1-x^(k+5))/(x^(k+1)*(1-x^(k+5)) - 1/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Oct 18 2013
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 + 22*x^8 +...
%t nMax = 42; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x]&; A227374 = col[4][[1 ;; nMax]] (* _Jean-François Alcover_, Nov 03 2016 *)
%o (PARI) {a(n)=local(CF); CF=1+x; for(k=0, n, CF=1/(1 - x^(n-k+1)*(1 - x^(n-k+5))*CF+x*O(x^n))); polcoeff(CF, n)}
%o for(n=0,50,print1(a(n),", "))
%Y Cf. A173173, A227360, A227375, A228644, A228645.
%Y Column m=4 of A185646.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jul 09 2013
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