The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A160852 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A160852

Chebyshev transform of A107841.
(history; published version)

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

PROG

(MAGMAMagma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1+x-x^2-Sqrt(1-10*x-x^2+10*x^3+x^4))/(6*x*(1-x^2)))) // G. C. Greubel, Apr 30 2018

Discussion

Thu Sep 08

08:45

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

#25 by Vaclav Kotesovec at Tue May 01 06:55:15 EDT 2018

STATUS

reviewed

approved

#24 by Michel Marcus at Tue May 01 01:22:58 EDT 2018

STATUS

proposed

reviewed

#23 by G. C. Greubel at Mon Apr 30 23:14:08 EDT 2018

STATUS

editing

proposed

#22 by G. C. Greubel at Mon Apr 30 23:14:00 EDT 2018

FORMULA

G.f.: (1+x-x^2-sqrt(1-10x10*x-x^2+10x10*x^3+x^4))/(6x6*x*(1-x^2));.

a(n) = sumSum_{k=0..floor(n/2), } C(n-k,k)*A107841(n-2k2*k)}.

PROG

(PARI) x='x+O('x^30); Vec((1+x-x^2-sqrt(1-10*x-x^2+10*x^3+x^4))/(6*x*(1-x^2))) \\ G. C. Greubel, Apr 30 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1+x-x^2-Sqrt(1-10*x-x^2+10*x^3+x^4))/(6*x*(1-x^2)))) // G. C. Greubel, Apr 30 2018

STATUS

approved

editing

#21 by N. J. A. Sloane at Thu Feb 27 09:48:51 EST 2014

STATUS

reviewed

approved

#20 by Vaclav Kotesovec at Thu Feb 27 08:25:10 EST 2014

STATUS

proposed

reviewed

#19 by Vaclav Kotesovec at Thu Feb 27 08:25:04 EST 2014

STATUS

editing

proposed

#18 by Vaclav Kotesovec at Thu Feb 27 08:24:38 EST 2014

FORMULA

ConjectureRecurrence: n*(n+1)*a(n) = (n-5)*a(n-6) + 5*(2*n-17)*a(n-15) -n* (2*n-17)*a(n-24) +- 20*n*(n-2)*a(n-3) +n* (2*n-71)*a(n-42) -+ 5*n*(2*n-7)*a(n-5) -n*(n-51)*a(n-61) =0. - R. J. Mathar, Jul 24 2012, simplified by _Fung Lam_, Jan 27 2014

Recurrence: (n+1)*a(n) = (n-5)*a(n-6) + 5*(2*n-7)*a(n-5) - (2*n-7)*a(n-4) - 20*(n-2)*a(n-3) + (2*n-1)*a(n-2) + 5*(2*n-1)*a(n-1). - Fung Lam, Jan 27 2014 (Identical to Mathar's except multiplication factor n.)

#17 by Vaclav Kotesovec at Thu Feb 27 08:21:34 EST 2014

FORMULA

a(n) ~ r*(r+10) * sqrt(10*r^3-2*r^2-30*r+4) / (12 * sqrt(Pi) * n^(3/2) * r^(n+1)), where r = 1 / (5/2 + sqrt(6) + 1/2*sqrt(53+20*sqrt(6))) = 0.100010105114224353... - Vaclav Kotesovec, Feb 27 2014

STATUS

proposed

editing