login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127211 a(n) = 4^n*Lucas(n), where Lucas = A000204. 10
4, 48, 256, 1792, 11264, 73728, 475136, 3080192, 19922944, 128974848, 834666496, 5402263552, 34963718144, 226291089408, 1464583847936, 9478992822272, 61349312856064, 397061136580608, 2569833552019456, 16632312393367552 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1225

Index entries for linear recurrences with constant coefficients, signature (4,16).

FORMULA

a(n) = Trace of matrix [({4,4},{4,0})^n].

a(n) = 4^n * Trace of matrix [({1,1},{1,0})^n].

From Colin Barker, Sep 02 2013: (Start)

a(n) = 4*a(n-1) + 16*a(n-2).

G.f.: -4*x*(8*x+1)/(16*x^2+4*x-1). (End)

MATHEMATICA

Table[4^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]

Table[4^n*LucasL[n], {n, 1, 50}] (* G. C. Greubel, Dec 18 2017 *)

PROG

(PARI) x='x + O('x^30); Vec(-4*x*(8*x+1)/(16*x^2+4*x-1)) \\ G. C. Greubel, Dec 18 2017

(MAGMA) [4^n*LUcas(n): n in [1..30]]; // G. C. Greubel, Dec 18 2017

CROSSREFS

Cf. A000204, A087131, A127210, A127212, A127213, A127214, A127215, A127216.

Sequence in context: A275138 A273767 A292074 * A274729 A217153 A129002

Adjacent sequences:  A127208 A127209 A127210 * A127212 A127213 A127214

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Jan 09 2007

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)