The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A190974

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A190974

a(n) = 7*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
(history; published version)

#27 by Peter Luschny at Sat Jun 11 03:33:53 EDT 2022

STATUS

reviewed

approved

#26 by Kevin Ryde at Sat Jun 11 01:52:00 EDT 2022

STATUS

proposed

reviewed

#25 by Kevin Ryde at Sat Jun 11 01:51:43 EDT 2022

STATUS

editing

proposed

#24 by Kevin Ryde at Sat Jun 11 01:50:59 EDT 2022

FORMULA

G.f.: x/(1 - 7x 7*x + 5*x^2). - Philippe Deléham, Oct 12 2011

KEYWORD

nonn,easy,changed

STATUS

proposed

editing

#23 by G. C. Greubel at Sat Jun 11 01:03:21 EDT 2022

STATUS

editing

proposed

#22 by G. C. Greubel at Sat Jun 11 01:02:43 EDT 2022

LINKS

G. C. Greubel, <a href="/A190974/b190974.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7, -5).

FORMULA

From G. C. Greubel, Jun 11 2022: (Start)

a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 7/(2*sqrt(5))).

E.g.f.: (2/sqrt(29))*exp(7*x/2)*sinh(sqrt(29)*x/2). (End)

PROG

(Magma) [n le 2 select n-1 else 7*Self(n-1) - 5*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022

(SageMath) [lucas_number1(n, 7, 5) for n in (0..50)] # G. C. Greubel, Jun 11 2022

STATUS

approved

editing

#21 by Bruno Berselli at Thu Nov 26 05:49:38 EST 2015

STATUS

reviewed

approved

#20 by Michel Marcus at Thu Nov 26 04:44:47 EST 2015

STATUS

proposed

reviewed

#19 by Jon E. Schoenfield at Thu Nov 26 03:38:44 EST 2015

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Thu Nov 26 03:38:42 EST 2015

FORMULA

a(n) = ((7/2 + 1/2*sqrt(29))^n - (7/2 - 1/2*sqrt(29))^n)/sqrt(29). [- _Giorgio Balzarotti, _, May 28 2011]

G.f.: x/(1 - 7x + 5*x^2). - From __Philippe Deléham_, Oct 12 2011.

CROSSREFS

Cf. A190958 (index to generalized Fibonacci sequences).

STATUS

approved

editing