login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)