The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A341544 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A341544

a(n) = sqrt( Product_{j=1..n} Product_{k=1..4} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/4)^2) ).
(history; published version)

#13 by Vaclav Kotesovec at Sun Feb 14 05:53:11 EST 2021

STATUS

reviewed

approved

#12 by Joerg Arndt at Sun Feb 14 04:56:36 EST 2021

STATUS

proposed

reviewed

#11 by Vaclav Kotesovec at Sun Feb 14 04:32:48 EST 2021

STATUS

editing

proposed

#10 by Vaclav Kotesovec at Sun Feb 14 04:32:34 EST 2021

FORMULA

From Vaclav Kotesovec, Feb 14 2021: (Start)

G.f.: 4*(4 - 67*x + 197*x^2 - 107*x^3 + 9*x^4) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).

a(n) = 6 + 4*(2 + sqrt(3))^n + 4*(2 - sqrt(3))^n + (7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n. (End)

#9 by Vaclav Kotesovec at Sun Feb 14 04:29:56 EST 2021

MATHEMATICA

Table[6 + 4 (2 + Sqrt[3])^n + 4 (2 - Sqrt[3])^n + (7 + 4 Sqrt[3])^n + (7 - 4 Sqrt[3])^n, {n, 1, 20}] // FullSimplify (* Vaclav Kotesovec, Feb 14 2021 *)

STATUS

proposed

editing

#8 by Seiichi Manyama at Sun Feb 14 04:05:58 EST 2021

STATUS

editing

proposed

#7 by Seiichi Manyama at Sun Feb 14 03:26:24 EST 2021

LINKS

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (19, -76, 76, -19, 1)

#6 by Seiichi Manyama at Sun Feb 14 02:41:56 EST 2021

CROSSREFS

Column k=4 of A341533.

#5 by Seiichi Manyama at Sun Feb 14 01:53:45 EST 2021

FORMULA

a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5).

#4 by Seiichi Manyama at Sun Feb 14 01:49:10 EST 2021

FORMULA

a(n) = .

a(n) = 18*a(n-1) - 58*a(n-2) + 18*a(n-3) - a(n-4) + 144.