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A190959 a(n) = 3*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1. 2
0, 1, 3, 4, -3, -29, -72, -71, 147, 796, 1653, 979, -5328, -20879, -35997, -3596, 169197, 525571, 730728, -435671, -4960653, -12703604, -13307547, 23595379, 137323872, 293994721, 195364803, -883879196, -3628461603, -6465988829, -1255658472, 28562968729 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is the Lucas U(P=3, Q=5) sequence. - R. J. Mathar, Oct 24 2012

a(n+2)/a(n+1) equals the continued fraction 3 - 5/(3 - 5/(3 - 5/(3 - ... - 5/3))) with n 5's. - Greg Dresden, Oct 06 2019

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Wikipedia, Lucas sequence

Index entries for linear recurrences with constant coefficients, signature (3,-5).

FORMULA

a(n) = (1/11)*i*sqrt(11)*((3/2 - (1/2)*i*sqrt(11))^n - (3/2 + (1/2)*i*sqrt(11))^n), where i = sqrt(-1). - Paolo P. Lava, Jun 01 2011

G.f.: x/(1 - 3*x + 5*x^2). - Philippe Deléham, Oct 11 2011

E.g.f.: 2*exp(3*x/2)*sin(sqrt(11)*x/2)/sqrt(11). - Stefano Spezia, Oct 06 2019

MATHEMATICA

LinearRecurrence[{3, -5}, {0, 1}, 50]

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3x+5*x^2))) \\ G. C. Greubel, Jan 25 2018

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 5*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018

CROSSREFS

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A287463 A288404 A287986 * A038018 A108658 A240669

Adjacent sequences:  A190956 A190957 A190958 * A190960 A190961 A190962

KEYWORD

sign,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 24 2011

STATUS

approved

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Last modified February 25 08:05 EST 2020. Contains 332221 sequences. (Running on oeis4.)