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A048696
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Generalized Pellian with second term equal to 9.
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A164587. Inverse binomial transform of A164298. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n)=2*a(n-1)+a(n-2); a(0)=1, a(1)=9.
G.f.: (1+7*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=binomial transform of 5,6,10,12,20,24,40 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009]
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EXAMPLE
| a(n)=[ (4*sqrt(2)+1)(1+sqrt(2))^n - (4*sqrt(2)-1)(1-sqrt(2))^n ]/2
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MAPLE
| with(combinat): a:=n->7*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{8}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
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PROG
| (MAGMA) [ n le 2 select 8*n-7 else 2*Self(n-1)+Self(n-2): n in [1..28] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009]
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CROSSREFS
| Cf. A001333, A000129, A048654, A048655.
Sequence in context: A058510 A043122 A043902 * A046103 A146459 A041158
Adjacent sequences: A048693 A048694 A048695 * A048697 A048698 A048699
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 17 2009
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