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A155127 a(n) = 6*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=5, a(2)=35. 10
1, 5, 35, 240, 1650, 11340, 77940, 535680, 3681720, 25304400, 173916720, 1195326720, 8215460640, 56464724160, 388081108800, 2667274997760, 18332136639360, 125996469822720, 865971638772480, 5951808651571200 (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 (6,6).

FORMULA

G.f.: (1-x-x^2)/(1-6*x-6*x^2) .

a(n) = (2/3)*sqrt(15)*((3+sqrt(15))^(n-1) - (3-sqrt(15))^(n-1)) + (5/2)*((3+sqrt(15))^(n-1) + (3-sqrt(15))^(n-1)) + (1/6)*[binomial(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jan 26 2009

a(n) = (1/6)*[n=0] - 5*(sqrt(6)*i)^(n-2)*ChebyshevU(n, -sqrt(6)*i/2). - G. C. Greubel, Mar 25 2021

MAPLE

m:=6; 1, seq(simplify((1-m)*(sqrt(m)*I)^(n-2)*ChebyshevU(n, -I*sqrt(m)/2)), n = 1..30); # G. C. Greubel, Mar 25 2021

MATHEMATICA

LinearRecurrence[{6, 6}, {1, 5, 35}, 20] (* Harvey P. Dale, Apr 14 2015 *)

PROG

(Magma) m:=6; [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=6; [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), A155119 (m=5), this sequence (m=6), A155130 (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).

Sequence in context: A091928 A305739 A290903 * A239846 A193577 A196661

Adjacent sequences:  A155124 A155125 A155126 * A155128 A155129 A155130

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 20 2009

STATUS

approved

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Last modified May 13 03:13 EDT 2021. Contains 343836 sequences. (Running on oeis4.)