A289260 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=8/5.

1, 3, 5, 9, 17, 30, 52, 90, 154, 262, 446, 758, 1286, 2182, 3702, 6278, 10646, 18054, 30614, 51910, 88022, 149254, 253078, 429126, 727638, 1233798, 2092054, 3547334, 6014934, 10199046, 17293718, 29323590, 49721686, 84309126, 142956310, 242399686, 411017942

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,-2).

Crossrefs

Cf. A078140 (includes guide to related sequences), A289265.

Cf. A279780.

Programs

Mathematica

r = 8/5;
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,-2},{1,3,5,9,17,30,52},40] (* Harvey P. Dale, Oct 13 2023 *)

PARI

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

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r](-x)^k), where r = 8/5 and [ ] = floor.

From Colin Barker, Jul 14 2017: (Start)

G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4) / ((1 - x)*(1 - x - 2*x^3)).

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-4) for n>3.

(End)

a(n) = abs(A279780(n)). - Alois P. Heinz, Jul 15 2017