A288236 Coefficients in the expansion of 1/([r]-[2*r]*x+[3*r]*x^2-...); [ ]=floor, r=-4/5+sqrt(6).

1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 493, 865, 1518, 2664, 4675, 8204, 14397, 25265, 44337, 77805, 136534, 239592, 420441, 737798, 1294700, 2271961, 3986877, 6996242, 12277127, 21544115, 37805987, 66342603, 116419152, 204294349, 358499270, 629100742

Offset: 0

Author

Clark Kimberling, Jul 11 2017

Keywords

• nonn
• easy

Comments

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

Conjecture: the sequence is strictly increasing.

Crossrefs

Cf. A078140 (includes guide to related sequences), A288235.

Programs

Mathematica

r = -4/5 + Sqrt[6];
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 = -4/5 + sqrt(6) and [ ] = floor.