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Search: id:A118658
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| A118658 |
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L_n - F_n where L_n is the Lucas Number and F_n is the Fibonacci Number. |
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+0
3
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| 2, 0, 2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Essentially the same as A006355, A047992, A054886, A055389, A068922, A090991, - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(0)=2, a(1)=0, a(n)=a(n-1)+a(n-2)for n>1 . G.f. (2-2*x)/(1-x-x^2) . a(0)=2 and a(n)= 2*A000045(n-1) for n>0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006
a(n)=F(n)+F(n+3) n>=-3 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
Closed form. a(n)=[(1/2)+(1/2)*sqrt(5)]^n-(1/5*[(1/2)+(1/2)*sqrt(5)]^n*sqrt(5)+(1/5)*sqrt(5)*[(1/2)-(1/2) *sqrt(5)]^n+[(1/2)-(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
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EXAMPLE
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L_7 = 18, F_7 = 8, L_7 - F_7 = 10
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MAPLE
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BB := n->if n=0 then 2; > elif n=1 then 0; > else BB(n-2)+BB(n-1); > fi: > L:=[]: for k from 0 to 38 do L:=[op(L), BB(k)]: od: L; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
with(combinat): seq(fibonacci(n)+fibonacci(n+3), n=-3..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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CROSSREFS
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Cf. A000032, A003714.
Sequence in context: A157898 A137430 A002121 this_sequence A165912 A071055 A078052
Adjacent sequences: A118655 A118656 A118657 this_sequence A118659 A118660 A118661
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KEYWORD
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easy,nonn
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AUTHOR
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Bill Jones (b92057(AT)yahoo.com), May 18 2006
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EXTENSIONS
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More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 01 2006
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