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

Author

Clark Kimberling, Jul 18 2017

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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];

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