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%I #15 Jul 13 2017 11:09:12
%S 1,3,5,9,17,30,52,91,160,281,493,865,1518,2664,4675,8204,14397,25265,
%T 44337,77806,136540,239611,420488,737905,1294933,2272449,3987870,
%U 6998224,12281027,21551700,37820597,66370521,116472145,204394366,358687108,629451995
%N Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=sqrt(11/4).
%C Conjecture: the sequence is strictly increasing.
%H Robert Israel, <a href="/A288237/b288237.txt">Table of n, a(n) for n = 0..4089</a>
%F G.f.: 1/(Sum_{k>=0} [(k+1)*r)](-x)^k), where r = sqrt(11/4) and [ ] = floor.
%p N:= 100: # to get a(0)..a(N)
%p r:= sqrt(11/4):
%p G:= 1/add(floor((k+1)*r)*(-x)^k,k=0..N):
%p S:= series(G,x,N+1):
%p seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Jul 13 2017
%t r = Sqrt[11/4];
%t u = 1000; (* # initial terms from given series *)
%t v = 100; (* # coefficients in reciprocal series *)
%t CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]
%Y Cf. A078140 (includes guide to related sequences).
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jul 11 2017