A048696 Generalized Pellian with second term equal to 9.

1, 9, 19, 47, 113, 273, 659, 1591, 3841, 9273, 22387, 54047, 130481, 315009, 760499, 1836007, 4432513, 10701033, 25834579, 62370191, 150574961, 363520113, 877615187, 2118750487, 5115116161, 12348982809, 29813081779, 71975146367

Offset

0,2

Comments

Binomial transform of 5,6,10,12,20,24,40. - Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009

Binomial transform of A164587. Inverse binomial transform of A164298. - Klaus Brockhaus, Aug 17 2009

For n > 0: a(n) = A105082(n) - A105082(n-1). - Reinhard Zumkeller, Dec 15 2013

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 (2,1).

Formula

a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=9.

a(n) = ((4*sqrt(2)+1)(1+sqrt(2))^n - (4*sqrt(2)-1)(1-sqrt(2))^n)/2.

G.f.: (1+7*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008

Maple

with(combinat): a:=n->7*fibonacci(n, 2)+fibonacci(n+1, 2): seq(a(n), n=0..25); # Zerinvary Lajos, Apr 04 2008

Mathematica

a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{8}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 9}, 30] (* Harvey P. Dale, Apr 20 2012 *)

Prog

(Magma) [ n le 2 select 8*n-7 else 2*Self(n-1)+Self(n-2): n in [1..28] ]; // Klaus Brockhaus, Aug 17 2009
(Maxima) a[0]:1$
a[1]:9$
a[n]:=2*a[n-1]+a[n-2]$
A048696(n):=a[n]$
makelist(A048696(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
(Haskell)
a048696 n = a048696_list !! n
a048696_list = 1 : 9 : zipWith (+)
               a048696_list (map (2 *) $ tail a048696_list)
-- Reinhard Zumkeller, Dec 15 2013

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Sequence in context: A058510 A043122 A043902 * A046103 A146459 A308025

Adjacent sequences: A048693 A048694 A048695 * A048697 A048698 A048699

Keyword

easy,nonn

Author

Barry E. Williams

Status

approved