login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048877 a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8. 2
1, 8, 33, 140, 593, 2512, 10641, 45076, 190945, 808856, 3426369, 14514332, 61483697, 260449120, 1103280177, 4673569828, 19797559489, 83863807784, 355252790625, 1504874970284, 6374752671761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Generalized Pellian with second term of 8.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (4,1).

FORMULA

a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).

G.f.: (1+4*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008

a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.

MAPLE

with(combinat): a:=n->4*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008

MATHEMATICA

CoefficientList[Series[(1+4x)/(1-4x-x^2), {x, 0, 20}], x]  (* Harvey P. Dale, Mar 30 2011 *)

LinearRecurrence[{4, 1}, {1, 8}, 30] (* Harvey P. Dale, Nov 03 2013 *)

PROG

(Haskell)

a048877 n = a048877_list !! n

a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)

-- Reinhard Zumkeller, May 01 2013

CROSSREFS

Cf. A015448, A001076, A001077, A033887.

Sequence in context: A222346 A283544 A212404 * A220590 A001407 A005398

Adjacent sequences:  A048874 A048875 A048876 * A048878 A048879 A048880

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 05:01 EST 2017. Contains 294988 sequences.