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Revision History for A275195

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A275195

Sum of n-th powers of the roots of x^3 - 7*x^2 - 49*x - 49.
(history; published version)

#27 by Harvey P. Dale at Sun Jan 01 14:51:33 EST 2023

STATUS

editing

approved

#26 by Harvey P. Dale at Sun Jan 01 14:51:30 EST 2023

MATHEMATICA

LinearRecurrence[{7, 49, 49}, {3, 7, 147}, 30] (* Harvey P. Dale, Jan 01 2023 *)

STATUS

approved

editing

#25 by Bruno Berselli at Thu Aug 11 10:14:32 EDT 2016

STATUS

editing

approved

#24 by Bruno Berselli at Thu Aug 11 10:14:26 EDT 2016

FORMULA

a(n) = (-sqrt(7)*tan(Pi/7))^n + (-sqrt(7)*tan(2*Pi/7))^n + (-sqrt(7)*tan(4*Pi/7))^n for n >= 0.

a(0) = 3, a(1) = 7, a(2) = 147; thereafter a(n) = 7*a(n-1) + 49*a(n-2) + 49*a(n-3).

a(n) = (-sqrt(7)*tan(Pi/7))^n + (-sqrt(7)*tan(2*Pi/7))^n + (-sqrt(7)*tan(4*Pi/7))^n.

a(0)=3, a(1)=7, a(2)=147; thereafter a(n) = 7*a(n-1) + 49*a(n-2) + 49*a(n-3).

STATUS

approved

editing

#23 by Bruno Berselli at Sat Jul 23 09:49:30 EDT 2016

STATUS

reviewed

approved

#22 by Michel Marcus at Sat Jul 23 08:42:18 EDT 2016

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proposed

reviewed

#21 by Colin Barker at Sat Jul 23 08:17:28 EDT 2016

STATUS

editing

proposed

#20 by Colin Barker at Sat Jul 23 08:16:55 EDT 2016

LINKS

Colin Barker, <a href="/A275195/b275195.txt">Table of n, a(n) for n = 0..900</a>

PROG

(PARI) Vec((1-7*x)*(3+7*x)/(1-7*x-49*x^2-49*x^3) + O(x^30)) \\ Colin Barker, Jul 23 2016

STATUS

approved

editing

#19 by Charles R Greathouse IV at Wed Jul 20 23:57:15 EDT 2016

STATUS

editing

approved

#18 by Charles R Greathouse IV at Wed Jul 20 23:57:11 EDT 2016

FORMULA

G.f.: (-49*x^2-14*x+3)/(-49*x^3-49*x^2-7*x+1).

CROSSREFS

Cf. A108716, A215794.

STATUS

approved

editing