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A048697
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Generalized Pellian with second term equal to 10.
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2
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1, 10, 21, 52, 125, 302, 729, 1760, 4249, 10258, 24765, 59788, 144341, 348470, 841281, 2031032, 4903345, 11837722, 28578789, 68995300, 166569389, 402134078, 970837545, 2343809168, 5658455881
(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)=10
G.f.: (1+8*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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EXAMPLE
| a(n)=[ (9+sqrt(2))(1+sqrt(2))^n - (9-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2)
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MAPLE
| with(combinat): a:=n->8*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].{{9}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
LinearRecurrence[{2, 1}, {1, 10}, 35] (* From Harvey P. Dale, Jul 26 2011 *)
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CROSSREFS
| Cf. A001333, A000129, A048654, A048655.
Sequence in context: A122963 A067520 A042309 * A090076 A156592 A045973
Adjacent sequences: A048694 A048695 A048696 * A048698 A048699 A048700
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams
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