A289261 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=13/8.

1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 494, 871, 1537, 2711, 4782, 8437, 14885, 26258, 46320, 81712, 144145, 254277, 448555, 791273, 1395843, 2462330, 4343664, 7662429, 13516885, 23844416, 42062667, 74200520, 130893196, 230901729, 407321472, 718534172

Offset

0,2

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,-2,1,-2,2).

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = 13/8 and [ ] = floor.

G.f.: (1 - x)*(1 + x)^2*(1 + x^2)*(1 + x^4) / (1 - 2*x + x^2 - 2*x^3 + 2*x^4 - x^5 + 2*x^6 - 2*x^7). - Colin Barker, Jul 14 2017

Mathematica

r = 13/8;
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, -2, 2}, {1, 3, 5, 9, 17, 30, 52, 91, 160, 281}, 40] (* Harvey P. Dale, Aug 04 2024 *)

Prog

(PARI) Vec((1 - x)*(1 + x)^2*(1 + x^2)*(1 + x^4) / (1 - 2*x + x^2 - 2*x^3 + 2*x^4 - x^5 + 2*x^6 - 2*x^7) + O(x^50)) \\ Colin Barker, Jul 20 2017

Crossrefs

Cf. A078140 (includes guide to related sequences), A289266.

Sequence in context: A288234 A288233 A288232 * A357549 A143373 A282184

Adjacent sequences: A289258 A289259 A289260 * A289262 A289263 A289264

Keyword

nonn,easy

Author

Clark Kimberling, Jul 14 2017

Status

approved