A288236 - OEIS

%I #8 Jul 13 2017 21:18:36

%S 1,3,5,9,17,30,52,91,160,281,493,865,1518,2664,4675,8204,14397,25265,

%T 44337,77805,136534,239592,420441,737798,1294700,2271961,3986877,

%U 6996242,12277127,21544115,37805987,66342603,116419152,204294349,358499270,629100742

%N Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=-4/5+sqrt(6).

%C A288235(k) = a(k) if and only if k <= 56.

%C Conjecture: the sequence is strictly increasing.

%F G.f.: 1/(Sum_{k>=0} [(k+1)*r)](-x)^k), where r = -4/5 + sqrt(6) and [ ] = floor.

%t r = -4/5 + Sqrt[6];

%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