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A048696
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Generalized Pellian with second term equal to 9.
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6
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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
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MAPLE
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with(combinat): a:=n->7*fibonacci(n, 2)+fibonacci(n+1, 2): seq(a(n), n=0..25); # Zerinvary Lajos, Apr 04 2008
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A001333, A000129, A048654, A048655.
Sequence in context: A058510 A043122 A043902 * A046103 A146459 A308025
Adjacent sequences: A048693 A048694 A048695 * A048697 A048698 A048699
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams
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STATUS
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approved
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