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A221174
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a(0)=-4, a(1)=5; thereafter a(n) = 2*a(n-1) + a(n-2).
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6
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-4, 5, 6, 17, 40, 97, 234, 565, 1364, 3293, 7950, 19193, 46336, 111865, 270066, 651997, 1574060, 3800117, 9174294, 22148705, 53471704, 129092113, 311655930, 752403973, 1816463876, 4385331725, 10587127326, 25559586377, 61706300080, 148972186537, 359650673154
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368, 2012
Index entries for linear recurrences with constant coefficients, signature (2,1).
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FORMULA
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a(n)=(1/4)*(9*sqrt(2)*((1+sqrt(2))^n-(1-sqrt(2))^n)-8*((1+sqrt(2))^n+(1-sqrt(2))^n)). - Paolo P. Lava, Jan 04 2013
a(n) = 13*A000129(n)-4*A000129(n+1). - R. J. Mathar, Jan 14 2013
G.f.: -(13*x-4) / (x^2+2*x-1). - Colin Barker, Jul 10 2015
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PROG
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(Haskell)
a221174 n = a221174_list !! n
a221174_list = -4 : 5 : zipWith (+)
(map (* 2) $ tail a221174_list) a221174_list
-- Reinhard Zumkeller, Jan 04 2013
(PARI) Vec(-(13*x-4)/(x^2+2*x-1) + O(x^50)) \\ Colin Barker, Jul 10 2015
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CROSSREFS
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Cf. A000129, A078343, A221172, A221173, A221175.
Sequence in context: A217464 A235711 A010753 * A047195 A109889 A103518
Adjacent sequences: A221171 A221172 A221173 * A221175 A221176 A221177
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Jan 04 2013
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STATUS
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approved
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