A289262 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=11/7.

1, 3, 5, 9, 18, 36, 71, 138, 268, 522, 1017, 1980, 3853, 7498, 14594, 28406, 55287, 107604, 209429, 407614, 793344, 1544090, 3005269, 5849172, 11384281, 22157298, 43124882, 83934214, 163361667, 317951804, 618831521, 1204435526, 2344200136, 4562530890

Offset: 0

Author

Clark Kimberling, Jul 14 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-1,2,-2).

Crossrefs

Cf. A078140 (includes guide to related sequences), A289267.

Programs

Mathematica

r = 11/7;
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]
LinearRecurrence[{2,-1,2,-1,2,-2},{1,3,5,9,18,36,71,138,268},40] (* Harvey P. Dale, Jun 11 2024 *)

PARI

Vec((1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6) + O(x^50)) \\ Colin Barker, Jul 20 2017

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = 11/7 and [ ] = floor.

G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6). - Colin Barker, Jul 14 2017