A288234 Coefficients in the expansion of 1/([r]-[2*r]*x+[3*r]*x^2-...); [ ]=floor, r=-1+sqrt(7).

1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 493, 865, 1518, 2664, 4675, 8204, 14398, 25271, 44356, 77853, 136647, 239844, 420976, 738898, 1296915, 2276349, 3995455, 7012834, 12308945, 21604693, 37920614, 66558359, 116823399, 205048721, 359902025, 631700929

Offset: 0

Author

Clark Kimberling, Jul 11 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Examples

			G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = -1+sqrt(7) and [ ] = floor.
		

Crossrefs

Cf. A078140 (includes guide to related sequences).

Programs

Mathematica

r = -1 + Sqrt[7];
u = 1000; (* # initial terms from given series *)
v = 100;   (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]