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A048877
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a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
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2
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1, 8, 33, 140, 593, 2512, 10641, 45076, 190945, 808856, 3426369, 14514332, 61483697, 260449120, 1103280177, 4673569828, 19797559489, 83863807784, 355252790625, 1504874970284, 6374752671761
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OFFSET
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0,2
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COMMENTS
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Generalized Pellian with second term of 8.
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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 (4,1).
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FORMULA
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a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).
G.f.: (1+4*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008
a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
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MAPLE
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with(combinat): a:=n->4*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
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MATHEMATICA
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CoefficientList[Series[(1+4x)/(1-4x-x^2), {x, 0, 20}], x] (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{4, 1}, {1, 8}, 30] (* Harvey P. Dale, Nov 03 2013 *)
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PROG
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(Haskell)
a048877 n = a048877_list !! n
a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)
-- Reinhard Zumkeller, May 01 2013
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CROSSREFS
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Cf. A015448, A001076, A001077, A033887.
Sequence in context: A317017 A283544 A212404 * A349101 A297683 A346819
Adjacent sequences: A048874 A048875 A048876 * A048878 A048879 A048880
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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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