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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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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, 78176338
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Essentially the same as A006355, A047992, A054886, A055389, A068922, A090991, - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,1).
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FORMULA
| 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 (paoloplava(AT)gmail.com), Nov 19 2008]
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EXAMPLE
| L_7 = 18, F_7 = 8, L_7 - F_7 = 10
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MAPLE
| 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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MATHEMATICA
| LinearRecurrence[{1, 1}, {2, 0}, 100] (* From Vladimir Joseph Stephan Orlovsky, June 05 2011 *)
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PROG
| (PARI) a(n)=fibonacci(n-1)<<1 \\ Charles R Greathouse IV, Jun 05, 2011
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CROSSREFS
| Cf. A000032, A000045, A003714.
Sequence in context: A137430 A181346 A002121 * A165912 A171936 A071055
Adjacent sequences: A118655 A118656 A118657 * A118659 A118660 A118661
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KEYWORD
| easy,nonn
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AUTHOR
| Bill Jones (b92057(AT)yahoo.com), May 18 2006
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EXTENSIONS
| 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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