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A048697
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Generalized Pellian with second term equal to 10.
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3
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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;
text;
internal format)
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OFFSET
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0,2
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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)=10.
a(n) = ((9+sqrt(2))(1+sqrt(2))^n - (9-sqrt(2))(1-sqrt(2))^n) / 2*sqrt(2).
G.f.: (1+8*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008
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MAPLE
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with(combinat): a:=n->8*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..25); # Zerinvary Lajos, Apr 04 2008
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MATHEMATICA
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a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{9}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 10}, 35] (* Harvey P. Dale, Jul 26 2011 *)
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PROG
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(Haskell)
a048697 n = a048697_list !! n
a048697_list = 1 : 10 : zipWith (+)
a048697_list (map (* 2) $ tail a048697_list)
-- Reinhard Zumkeller, Sep 05 2014
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CROSSREFS
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Cf. A001333, A000129, A048654, A048655.
Sequence in context: A219884 A042309 A215757 * A090076 A231966 A156592
Adjacent sequences: A048694 A048695 A048696 * A048698 A048699 A048700
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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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