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A048695
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Generalized Pellian with second term equal to 8.
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3
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1, 8, 17, 42, 101, 244, 589, 1422, 3433, 8288, 20009, 48306, 116621, 281548, 679717, 1640982, 3961681, 9564344, 23090369, 55745082, 134580533, 324906148, 784392829, 1893691806, 4571776441, 11037244688
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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)=8.
G.f.: (1+6*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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EXAMPLE
| a(n)=[ (7+sqrt(2))(1+sqrt(2))^n - (7-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2)
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MAPLE
| with(combinat): a:=n->6*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{7}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
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CROSSREFS
| Cf. A001333, A000129, A048654, A048655.
Sequence in context: A188129 A041849 A041124 * A153873 A111325 A173056
Adjacent sequences: A048692 A048693 A048694 * A048696 A048697 A048698
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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