Search: id:A061084
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%I A061084
%S A061084 1,2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,
%T A061084 15127,24476,39603,64079,103682,167761,271443,439204,710647,1149851,1860498,
%U A061084 3010349,4870847,7881196,12752043,20633239,33385282,54018521
%V A061084 1,2,-1,3,-4,7,-11,18,-29,47,-76,123,-199,322,-521,843,-1364,2207,-3571,
               5778,-9349,
%W A061084 15127,-24476,39603,-64079,103682,-167761,271443,-439204,710647,-1149851,
               1860498,
%X A061084 -3010349,4870847,-7881196,12752043,-20633239,33385282,-54018521
%N A061084 Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and 
               a(n) = a(n-2)-a(n-1).
%C A061084 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
%C A061084 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
%H A061084 T. D. Noe, <a href="b061084.txt">Table of n, a(n) for n=0..500</a>
%H A061084 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A061084 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A061084 a(n) = (-1)^(n-1) * ((n-1)-st Lucas number), see A000204
%F A061084 O.g.f.: (3*x+1)/(1+x-x^2). - Len Smiley (smiley(AT)math.uaa.alaska.edu), 
               Dec 02 2001
%e A061084 a(6) = a(4)-a(5) = -4 - 7 = -11
%Y A061084 Cf. A061083 for division, A000301 for multiplication and A000045 for 
               addition - the common Fibonacci numbers
%Y A061084 Sequence in context: A070827 A160191 A000032 this_sequence A055391 A134876 
               A019612
%Y A061084 Adjacent sequences: A061081 A061082 A061083 this_sequence A061085 A061086 
               A061087
%K A061084 sign,easy,nice
%O A061084 0,2
%A A061084 Ulrich Schimke (ulrschimke(AT)aol.com)
%E A061084 Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006

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