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Search: id:A127262
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| A127262 |
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a(0)=2, a(1)=2, a(n)=2*a(n-1)+12*a(n-2). |
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+0
2
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| 2, 2, 28, 80, 496, 1952, 9856, 43136, 204544, 926720, 4307968, 19736576, 91168768, 419176448, 1932378112, 8894873600, 40978284544, 188695052288, 869129519104, 4002599665664, 18434753560576, 84900703109120
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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If A091914(n-1)=F(n) the Fibonacci-like sequence, then a(n) is the Lucas-type sequence.
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FORMULA
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a(n)=((1+sqrt(13))^n-(1-sqrt(13)^n))/2/sqrt(13) G(x)=2*(1-x)/(1-2*x-12*x^2) E(x)=exp((1+sqrt(13))*x)+exp((1-sqrt(13))*x) a(n)=A091914(n)+12*A091914(n-2)
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MAPLE
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a[0]:=2:a[1]:=2:for i from 2 to 40 do a[i]:=2*a[i-1]+12*a[i-2] od: seq(a[n], n=0..40);
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PROGRAM
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(Other) sage: [lucas_number2(n, 2, -12) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
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Cf. A091914.
Sequence in context: A125067 A012000 A116091 this_sequence A121788 A018976 A074127
Adjacent sequences: A127259 A127260 A127261 this_sequence A127263 A127264 A127265
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Mar 27 2007
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