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A127226
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a(0)=2, a(1)=2, a(n)=2*a(n-1)+6*a(n-2).
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4
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2, 2, 16, 44, 184, 632, 2368, 8528, 31264, 113696, 414976, 1512128, 5514112, 20100992, 73286656, 267179264, 974078464, 3551232512, 12946935808, 47201266688, 172084148224, 627375896576, 2287256682496
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| If A083099(n-1)=F(n)=0,1,2,10,32... is the Fibonacci-type sequence, then a(n)=L(n) is the Lucas-type sequence. L(n)=F(n+1)+6*F(n-1)
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FORMULA
| G(x)=2*(1-x)/(1-6x-2x^2) E(x)=(exp((1+sqrt(7))x)+exp((1-sqrt(7))x)) a(n)=A083099(n)+6*A083099(n-2)
a(n)=[1+sqrt(7)]^n+[1-sqrt(7)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jul 31 2008]
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PROG
| (Other) sage: [lucas_number2(n, 2, -6) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
| Cf. A083099.
Sequence in context: A177832 A076615 A098777 * A001119 A062282 A012319
Adjacent sequences: A127223 A127224 A127225 * A127227 A127228 A127229
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Mar 26 2007
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