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%I #10 Jul 02 2019 22:46:32
%S 1,1,2,3,5,8,12,19,29,44,67,101,153,230,346,520,780,1171,1755,2631,
%T 3942,5905,8846,13247,19839,29707,44482,66604,99722,149309,223546,
%U 334692,501096,750226,1123216,1681635,2517676,3769356,5643307,8448900,12649289
%N G.f. is the continued fraction: A(x) = 1/[1 - x/[1 - (x-x^2)/[1 - (x^2-x^4)/[1 - (x^3-x^6)/[1-... - (x^n-x^(2n))/[1 - ... ]]]]]]].
%H Vaclav Kotesovec, <a href="/A099823/b099823.txt">Table of n, a(n) for n = 0..5000</a>
%F G.f.: A(x) = 1/(1-x*Sum_{n=0..inf} (-1)^n*[x^((3n+2)n) + x^((3n+1)(n+1))] ).
%F a(n) = Sum_{k=0..m} (-1)^[n/2] * a(n-1 - A001082(k)), where A001082(m) < n <= A001082(m+1).
%F a(n) ~ c * d^n, where d = 1.49715009102318386309178199346058484192024290343171764086663161717870056467... and c = 1.23439530191230647588567129689364633472692295156374785190689889414622... - _Vaclav Kotesovec_, Jul 01 2019
%e A(x) = 1/(1 - x*(1 + x - x^5 - x^8 + x^16 + x^21 - x^33 - x^40 + x^56 + x^65 - x^85 - x^96 ++-- ... + (-1)^[n/2]*x^A001082(n) +...)).
%e a(n) = a(n-1) + a(n-2) - a(n-6) - a(n-9) + a(n-17) + a(n-22) --++...
%t nmax = 50; CoefficientList[Series[1/(1 - x*Sum[(-1)^k*(x^((3*k+2)*k) + x^((3*k+1)*(k+1))), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 01 2019 *)
%Y Cf. A001082.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 26 2004
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