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Search: id:A108851
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| A108851 |
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a(n) = 4a(n-1) + 3a(n-2), a(0) = 1, a(1) = 2. |
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+0
2
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| 1, 2, 11, 50, 233, 1082, 5027, 23354, 108497, 504050, 2341691, 10878914, 50540729, 234799658, 1090820819, 5067682250, 23543191457, 109375812578, 508132824683, 2360658736466, 10967033419913, 50950109889050
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A083098, second binomial transform of (1, 0, 7, 0, 49, 0, 243, 0, ..).
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FORMULA
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a(n) = ((2 + sqrt(7))^n + (2 - sqrt(7))^n) / 2.
G.f.: (1 - 2x) / (1 - 4x - 3x^2).
E.g.f.: exp(2x)cosh(sqrt(7)x).
a(n+1)/a(n) converges to 2 + sqrt(7) = 4.645751311064...
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PROGRAM
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(Other) sage: [lucas_number2(n, 4, -3)/2 for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
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Cf. A080042 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
Sequence in context: A036996 A151314 A154415 this_sequence A105486 A137960 A018933
Adjacent sequences: A108848 A108849 A108850 this_sequence A108852 A108853 A108854
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 11 2005
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