A289246 - OEIS

%I #11 Aug 13 2017 22:55:27

%S 1,4,11,32,94,272,786,2272,6564,18962,54780,158254,457174,1320712,

%T 3815354,11022024,31841080,91984410,265730044,767656774,2217652596,

%U 6406486864,18507440702,53465396640,154454021166,446195972602,1288997492332,3723732703246

%N Coefficients in the expansion of 1/Sum_{k >= 0} ([r*(k + 1)] + [s*(k + 1)]) * (-x)^k, where [ ] = floor, r = (1+sqrt(5))/2, s = 1/r.

%C Conjecture: the sequence is strictly increasing.

%F G.f.: 1/Sum_{k >= 0} ([r*(k + 1)] + [s*(k + 1)]) * (-x)^k, where [ ] = floor, r = (1+sqrt(5))/2, s = 1/r.

%t r = GoldenRatio; s = 1/GoldenRatio;

%t CoefficientList[Series[1/Sum[(Floor[r*(k + 1)] + Floor[s*(k + 1)]) (-x)^k, {k, 0, 1000}], {x, 0, 50}], x]

%Y Cf. A078140.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Aug 09 2017