A288230 Coefficients of 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = sqrt(5/2) and [ ] = floor.

1, 3, 5, 9, 18, 36, 71, 138, 268, 522, 1017, 1980, 3853, 7498, 14594, 28406, 55287, 107604, 209428, 407608, 793325, 1544042, 3005154, 5848902, 11383662, 22155913, 43121842, 83927627, 163347533, 317921733, 618768013, 1204302235, 2343921860, 4561952576

Offset: 0

Author

Clark Kimberling, Jul 10 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Crossrefs

Cf. A078140 (includes guide to related sequences).

Programs

Mathematica

r = Sqrt[5/2];
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]

Formula

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