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A080040
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a(n)=2a(n-1)+2a(n-2), a(0)=2, a(1)=2.
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30
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2, 2, 8, 20, 56, 152, 416, 1136, 3104, 8480, 23168, 63296, 172928, 472448, 1290752, 3526400, 9634304, 26321408, 71911424, 196465664, 536754176, 1466439680, 4006387712, 10945654784, 29904084992, 81699479552, 223207129088
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| G.f.: g(t)=(2-2t)/(1-2t-2t^2) a(n)=(1+sqrt(3))^n+(1-sqrt(3))^n
a(n)=2*A026150(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
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MATHEMATICA
| CoefficientList[Series[(2 - 2t)/(1 - 2t - 2t^2), {t, 0, 30}], t]
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PROG
| sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(2, 2, 2, 2, lambda n: 0) sage: [it.next() for i in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
(Other) sage: [lucas_number2(n, 2, -2) for n in xrange(0, 27)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
(Haskell)
a080040 n = a080040_list !! n
a080040_list =
2 : 2 : map (* 2) (zipWith (+) a080040_list (tail a080040_list))
-- Reinhard Zumkeller, Oct 15 2011
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CROSSREFS
| Cf. A002605, A028859, A030195, A083337, A106435, A108898, A125145.
Sequence in context: A168506 A067640 A098277 * A060823 A178076 A137774
Adjacent sequences: A080037 A080038 A080039 * A080041 A080042 A080043
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003
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