A288231 Coefficients of 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = 4^(1/3) and [ ] = floor.

1, 3, 5, 9, 18, 36, 71, 138, 268, 522, 1017, 1981, 3859, 7517, 14642, 28521, 55557, 108223, 210814, 410654, 799931, 1558224, 3035341, 5912689, 11517614, 22435718, 43703622, 85132404, 165833537, 323035186, 629255898, 1225758065, 2387713549, 4651142959

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 = 4^(1/3) and [ ] = floor.