A289922 Coefficients of 1/([1+r] - [1+2r]x + [1+3r]x^2 - ...), where [ ] = floor and r = 19/21.

1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 2, -1, -5, -4, -1, 0, 0, 0, 0, 1, 1, -6, -15, -14, -6, -1, 0, 0, 0, 1, 0, -10, -21, -18, -7, -1, 0, 0, 0, 1, -1, -13, -20, -3, 18, 18, 7, 1, 0, 1, -2, -15, -13, 29

Offset: 0

Author

Clark Kimberling, Jul 18 2017

Keywords

• easy
• sign

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, -1, -1).

Crossrefs

Cf. A078140 (includes guide to related sequences), A289921, A289923.

Programs

Mathematica

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

PARI

Vec((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 + x^20 + x^21) + 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 = 19/21.

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 + x^20 + x^21). - Colin Barker, Jul 20 2017