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A061084
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Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2)-a(n-1).
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13
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1, 2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, -521, 843, -1364, 2207, -3571, 5778, -9349, 15127, -24476, 39603, -64079, 103682, -167761, 271443, -439204, 710647, -1149851, 1860498, -3010349, 4870847, -7881196, 12752043, -20633239, 33385282, -54018521
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OFFSET
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0,2
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COMMENTS
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If we drop 1 and start with 2 this is the Lucas sequence V(-1,-1). G.f.: (2+x)/(1+x-x^2). In this case a(n) is also the trace of A^(-n), where A is the Fibomatrix ((1,1), (1,0)). - Mario Catalani (mario.catalani(AT)unito.it), Aug 17 2002
The positive sequence with g.f. (1+x-2x^2)/(1-x-x^2) gives the diagonal sums of the Riordan array (1+2x,x/(1-x)). - Paul Barry, Jul 18 2005
Pisano period lengths: 1, 3, 8, 6, 4, 24, 16, 12, 24, 12, 10, 24, 28, 48, 8, 24, 36, 24, 18, 12,.... (is this A106291?) - R. J. Mathar, Aug 10 2012
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
Tanya Khovanova, Recursive Sequences
Wikipedia, Lucas sequence
Index entries for sequences related to linear recurrences with constant coefficients, signature (-1,1).
Index entries for Lucas sequences
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FORMULA
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a(n) = (-1)^(n-1) * A000204(n-1).
O.g.f.: (3*x+1)/(1+x-x^2). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 02 2001
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EXAMPLE
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a(6) = a(4)-a(5) = -4 - 7 = -11
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MATHEMATICA
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LinearRecurrence[{-1, 1}, {1, 2}, 40] (* From Harvey P. Dale, Nov 22 2011 *)
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CROSSREFS
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Cf. A061083 for division, A000301 for multiplication and A000045 for addition - the common Fibonacci numbers
Sequence in context: A070827 A160191 A000032 * A055391 A177940 A134876
Adjacent sequences: A061081 A061082 A061083 * A061085 A061086 A061087
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KEYWORD
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sign,easy,nice
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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Corrected by T. D. Noe, Oct 25 2006
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STATUS
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approved
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