The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A173150 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A173150

a(n) = sinh^2 (2n*arccosh(sqrt n)).
(history; published version)

#16 by Joerg Arndt at Sat Jun 23 12:19:24 EDT 2018

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Sat Jun 23 12:18:36 EDT 2018

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Sat Jun 23 12:18:34 EDT 2018

COMMENTS

Also a(n) = -Sin[sin(2n*ArcCos[Sqrt[arccos(sqrt(n]]])))^2 = -Sin[sin(2n*ArcSin[Sqrt[arcsin(sqrt(n]]])))^2.

STATUS

approved

editing

#13 by Vaclav Kotesovec at Tue Apr 05 08:51:59 EDT 2016

STATUS

editing

approved

#12 by Vaclav Kotesovec at Tue Apr 05 08:51:53 EDT 2016

EXTENSIONS

Minor edits by Vaclav Kotesovec, Apr 05 2016

#11 by Vaclav Kotesovec at Tue Apr 05 08:51:20 EDT 2016

MATHEMATICA

Table[Round[N[ - Sin[2 n ArcCos[Sqrt[n]]]^2, 100]], {n, 0, 20}] (* Artur Jasinski, Feb 11 2010 *)

#10 by Vaclav Kotesovec at Tue Apr 05 08:50:40 EDT 2016

CROSSREFS

Cf. A132592, A146311, A146312, A146313, A173115, A173116 , A173121, A173127, A173128, A173129, A173130, A173131, A173133, A173134, A173148.

STATUS

approved

editing

#9 by Alois P. Heinz at Sun Jun 29 13:12:39 EDT 2014

STATUS

proposed

approved

#8 by Michel Marcus at Sun Jun 29 09:47:33 EDT 2014

STATUS

editing

proposed

#7 by Michel Marcus at Sun Jun 29 09:47:26 EDT 2014

COMMENTS

Also a(n) = -Sin[2n*ArcCos[Sqrt[n]]]^2 = -Sin[2n*ArcSin[Sqrt[n]]]^2.

MAPLE

A173150 := proc(n) sinh(2*n*arccosh(sqrt(n))) ; %^2 ; expand(%) ; simplify(%) ; end proc: # _R. J. Mathar, _, Feb 26 2011

MATHEMATICA

Table[Round[N[ - Sin[2 n ArcCos[Sqrt[n]]]^2, 100]], {n, 0, 20}] (* _Artur Jasinski_, Feb 11 2010 *)

STATUS

proposed

editing