The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A026672 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A026672

a(n) = T(2n,n-1), T given by A026670. Also T(2n,n-1)=T(2n+1,n+2), T given by A026725; and T(2n,n-1), T given by A026736.
(history; published version)

#15 by Charles R Greathouse IV at Thu Sep 08 08:44:49 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^4/(2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 16 2019

Discussion

Thu Sep 08

08:44

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

#14 by Alois P. Heinz at Tue Jul 16 15:23:23 EDT 2019

STATUS

proposed

approved

#13 by Michel Marcus at Tue Jul 16 15:17:31 EDT 2019

STATUS

editing

proposed

#12 by Michel Marcus at Tue Jul 16 15:17:25 EDT 2019

CROSSREFS

Cf. A000108, A026670, A026725, A026736, A236830.

STATUS

proposed

editing

#11 by G. C. Greubel at Tue Jul 16 14:58:24 EDT 2019

STATUS

editing

proposed

#10 by G. C. Greubel at Tue Jul 16 14:57:35 EDT 2019

NAME

a(n) = T(2n,n-1), T given by A026670. Also T(2n,n-1)=T(2n+1,n+2), T given by A026725; and T(2n,n-1), T given by A026736.

OFFSET

1,2,2

LINKS

G. C. Greubel, <a href="/A026672/b026672.txt">Table of n, a(n) for n = 2..1000</a>

MATHEMATICA

Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^4/(2*(8*x^2 -(1-Sqrt[1-4*x] )^3)), {x, 0, 30}], x], 2] (* G. C. Greubel, Jul 16 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))) \\ G. C. Greubel, Jul 16 2019

(MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^4/(2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 16 2019

(Sage) a=((1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))).series(x, 30).coefficients(x, sparse=False); a[2:] # G. C. Greubel, Jul 16 2019

CROSSREFS

Cf. A236830.

STATUS

approved

editing

#9 by R. J. Mathar at Sat Aug 08 10:16:30 EDT 2015

STATUS

editing

approved

#8 by R. J. Mathar at Sat Aug 08 10:16:19 EDT 2015

FORMULA

Conjecture: -(n+1)*(n-6)*a(n) +2*(4*n^2-23*n+3)*a(n-1) +3*(-5*n^2+33*n-42)*a(n-2) -2*(2*n-3)*(n-5)*a(n-3)=0. - R. J. Mathar, Aug 08 2015

STATUS

approved

editing

#7 by Joerg Arndt at Sun Feb 02 03:59:44 EST 2014

STATUS

proposed

approved

#6 by Philippe Deléham at Sun Feb 02 03:23:21 EST 2014

STATUS

editing

proposed