A289923 Limiting sequence of coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r approaches 19/21 from the left.

1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 2, 7, 9, 5, 1, 0, 0, 0, 0, 0, 3, 12, 19, 15, 6, 1, 0, 0, 0, 0, 5, 22, 40, 39, 22, 7, 1, 0, 0, 0, 8, 39, 81, 94, 67, 30, 8, 1, 0, 0, 13, 69, 160, 214, 183, 104, 39, 9, 1, 0, 21, 121, 310, 468, 464

Offset

0,2

Comments

Conjecture: all the terms are nonnegative.

Links

Ray Chandler, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1).

Formula

G.f.: 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21-10^(-9).

G.f.: (1 + x)^2*(1 - x + x^2)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6)*(1 + x - x^3 - x^4 + x^6 - x^8 - x^9 + x^11 + x^12) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^11 + x^12 - x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19). - Colin Barker, Jul 20 2017

Mathematica

z = 2000; r = 19/21-10^(-9);
CoefficientList[Series[1/Sum[Floor[1 + (k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];

Crossrefs

Cf. A078140 (includes guide to related sequences), A289921, A289922.

Sequence in context: A356995 A289922 A017887 * A289921 A219482 A037859

Adjacent sequences: A289920 A289921 A289922 * A289924 A289925 A289926

Keyword

nonn,easy

Author

Clark Kimberling, Jul 18 2017

Status

approved