The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A116390 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A116390

Expansion of 1/(2*sqrt(1-4*x^2)-x-1).
(history; published version)

#32 by Charles R Greathouse IV at Thu Sep 08 08:45:24 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(2*Sqrt(1-4*x^2)-x-1) )); // G. C. Greubel, May 23 2019

Discussion

Thu Sep 08

08:45

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

#31 by N. J. A. Sloane at Thu Jan 30 21:29:15 EST 2020

FORMULA

D-finite with recurrence: -3*n*a(n) + 2*n*a(n-1) + (29*n-36)*a(n-2) + 8*(3-n)*a(n-3) + 68*(3-n)*a(n-4)=0. - R. J. Mathar, Aug 09 2012

Discussion

Thu Jan 30

21:29

OEIS Server: https://oeis.org/edit/global/2847

#30 by R. J. Mathar at Thu Jan 23 13:37:05 EST 2020

STATUS

editing

approved

#29 by R. J. Mathar at Thu Jan 23 13:35:56 EST 2020

FORMULA

ConjectureD-finite: -3*n*a(n) + 2*n*a(n-1) + (29*n-36)*a(n-2) + 8*(3-n)*a(n-3) + 68*(3-n)*a(n-4)=0. - R. J. Mathar, Aug 09 2012

STATUS

approved

editing

#28 by Alois P. Heinz at Sat May 25 11:03:23 EDT 2019

STATUS

proposed

approved

#27 by Sean A. Irvine at Fri May 24 04:39:32 EDT 2019

STATUS

editing

proposed

#26 by Sean A. Irvine at Fri May 24 04:39:20 EDT 2019

FORMULA

a(n) = Sum_{k=0..n} Sum_{j=0..k} Sum_{i=0..floor(n/2)} (-1)^(k-j)*C(k,j) *C(i+(j-1)/2,i)*C(j,n-2*i)*4^i .

Conjecture: -3*n*a(n) + 2*n*a(n-1) + (29*n-36)*a(n-2) + 8*(3-n)*a(n-3) + 68*(3-n)*a(n-4)=0. - R. J. Mathar, Aug 09 2012

STATUS

proposed

editing

#25 by Michel Marcus at Fri May 24 03:00:16 EDT 2019

STATUS

editing

proposed

#24 by Michel Marcus at Fri May 24 03:00:13 EDT 2019

EXAMPLE

Row sums of number triangle A116389.

CROSSREFS

Row sums of number triangle A116389.

STATUS

proposed

editing

#23 by G. C. Greubel at Thu May 23 22:52:31 EDT 2019

STATUS

editing

proposed