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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
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
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
KEYWORD
easy,nonn
STATUS
approved