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Search: id:A061084
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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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+0
12
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If we drop 1 and start with 2 this is the reflected (definition A074058) Lucas sequence with a(0)=2, a(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 (pbarry(AT)wit.ie), Jul 18 2005
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = (-1)^(n-1) * ((n-1)-st Lucas number), see A000204
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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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 this_sequence A055391 A134876 A019612
Adjacent sequences: A061081 A061082 A061083 this_sequence 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 (noe(AT)sspectra.com), Oct 25 2006
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