This site is supported by donations to The OEIS Foundation.

 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!)
 A048696 Generalized Pellian with second term equal to 9. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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 A041158 Adjacent sequences:  A048693 A048694 A048695 * A048697 A048698 A048699 KEYWORD easy,nonn AUTHOR 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.