The On-Line Encyclopedia of Integer Sequences (OEIS)

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A253262

Expansion of (x + x^2 + x^3) / (1 - x + x^2 - x^3 + x^4) in powers of x.
(history; published version)

#22 by Charles R Greathouse IV at Thu Sep 08 08:46:10 EDT 2022

PROG

(MAGMAMagma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x)*(1-x^3)/((1-x)*(1+x^5)))); // G. C. Greubel, Aug 02 2018

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#21 by Michael Somos at Thu Aug 02 23:24:32 EDT 2018

STATUS

editing

approved

#20 by Michael Somos at Thu Aug 02 23:24:12 EDT 2018

FORMULA

Euler transform of length 10 sequence [ 2, -1, -1, 0, -1, 0, 0, 0, 0, 1].

STATUS

proposed

editing

Discussion

Thu Aug 02

23:24

Michael Somos: Space edit.

#19 by Jon E. Schoenfield at Thu Aug 02 21:45:51 EDT 2018

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Thu Aug 02 21:45:49 EDT 2018

FORMULA

a(n) = f(n) / f(1) where f(n) := tan( am( n*x, m)) where x = 0.7379409146... and m = 1.3481185591... and am() is the Jacobi amplitude function.

STATUS

proposed

editing

#17 by Robert G. Wilson v at Thu Aug 02 15:53:34 EDT 2018

STATUS

editing

proposed

#16 by Robert G. Wilson v at Thu Aug 02 15:53:31 EDT 2018

COMMENTS

Cycle period is 10. - Robert G. Wilson v, Aug 02 2018

MATHEMATICA

CoefficientList[ Series[x (x^2 + x + 1)/(x^4 - x^3 + x^2 - x + 1), {x, 0, 75}], x] (* or *)

LinearRecurrence[{1, -1, 1, -1}, {0, 1, 2, 2}, 75] (* Robert G. Wilson v, Aug 02 2018 *)

STATUS

reviewed

editing

#15 by Michel Marcus at Thu Aug 02 14:57:42 EDT 2018

STATUS

proposed

reviewed

#14 by G. C. Greubel at Thu Aug 02 13:17:18 EDT 2018

STATUS

editing

proposed

#13 by G. C. Greubel at Thu Aug 02 13:17:12 EDT 2018

LINKS

G. C. Greubel, <a href="/A253262/b253262.txt">Table of n, a(n) for n = 0..2500</a>

MATHEMATICA

CoefficientList[Series[x*(1+x)*(1-x^3)/((1-x)*(1+x^5)), {x, 0, 60}], x] (* G. C. Greubel, Aug 02 2018 *)

PROG

(PARI) x='x+O('x^60); concat([0], Vec(x*(1+x)*(1-x^3)/((1-x)*(1+x^5)))) \\ G. C. Greubel, Aug 02 2018

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x)*(1-x^3)/((1-x)*(1+x^5)))); // G. C. Greubel, Aug 02 2018

STATUS

approved

editing