A289921 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 9/10.

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, 4, 16, 25, 19, 7, 1, 0, 0, 0, 0, 8, 36, 66, 63, 33, 9, 1, 0, 0, 0, 16, 80, 168, 192, 129, 51, 11, 1, 0, 0, 32, 176, 416, 552, 450, 231, 73, 13, 1, 0, 64, 384, 1008

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
• Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.
• Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, 1).

Crossrefs

Cf. A078140 (includes guide to related sequences), A289922, A289923.

Programs

Mathematica

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

PARI

Vec( (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10) + O(x^100)) \\ Colin Barker, Jul 21 2017

Formula

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

G.f.: (1 - x)*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4) / (1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 - x^10). - Colin Barker, Jul 20 2017