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A155119 a(n) = 5*a(n-1) + 5*a(n-2), n > 2, a(0)=1, a(1)=4, a(2)=24. 10
1, 4, 24, 140, 820, 4800, 28100, 164500, 963000, 5637500, 33002500, 193200000, 1131012500, 6621062500, 38760375000, 226907187500, 1328337812500, 7776225000000, 45522814062500, 266495195312500, 1560090046875000, 9132926210937500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

G.f.: (1 - x - x^2) / (1 - 5*x - 5*x^2).

a(n) = (14/15) * sqrt(5) * ((5/2 + (3/2)*sqrt(5))^(n-1) - (5/2 - (3/2)*sqrt(5))^(n-1)) + 2 * ((5/2 + (3/2)*sqrt(5))^(n-1) + (5/2 - (3/2)*sqrt(5))^(n-1)) + (1/5)*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jan 26 2009

a(n) = (1/5)*[n=0] - 4*(sqrt(5)*i)^(n-2)*ChebyshevU(n, -sqrt(5)*i/2). - G. C. Greubel, Mar 25 2021

MATHEMATICA

With[{m=5}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* G. C. Greubel, Mar 25 2021 *)

PROG

(Magma) m:=5; [1] cat [n le 2 select (m-1)*(m*n-(m-1)) else m*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 25 2021

(Sage) m=5; [1]+[-(m-1)*(sqrt(m)*i)^(n-2)*chebyshev_U(n, -sqrt(m)*i/2) for n in (1..30)] # G. C. Greubel, Mar 25 2021

CROSSREFS

Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), this sequence (m=5), A155127 (m=6), A155130 (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).

Sequence in context: A204199 A262376 A005319 * A114169 A121102 A307526

Adjacent sequences:  A155116 A155117 A155118 * A155120 A155121 A155122

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 20 2009

EXTENSIONS

a(20) corrected and a(21) from Sean A. Irvine, May 19 2019

STATUS

approved

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Last modified April 18 10:21 EDT 2021. Contains 343087 sequences. (Running on oeis4.)