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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A067150 A289922 A017887 * A289921 A219482 A037859

Adjacent sequences:  A289920 A289921 A289922 * A289924 A289925 A289926

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 18 2017

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)