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 A061084 Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2)-a(n-1). 20
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..4771 (terms 0..500 from T. D. Noe) Tanya Khovanova, Recursive Sequences Kai Wang, Fibonacci Numbers And Trigonometric Functions Outline, (2019). Q. Wang, On generalized Lucas sequences, Contemp. Math. 531 (2010) 127-141, Table 2 (k=2). Wikipedia, Lucas sequence Index entries for linear recurrences with constant coefficients, signature (-1,1). FORMULA a(n) = (-1)^(n-1) * A000204(n-1). O.g.f.: (3*x+1)/(1+x-x^2). - Len Smiley, Dec 02 2001 a(n) = A039834(n+1)+3*A039834(n). - R. J. Mathar, Oct 30 2015 EXAMPLE a(6) = a(4)-a(5) = -4 - 7 = -11. MATHEMATICA LinearRecurrence[{-1, 1}, {1, 2}, 40] (* Harvey P. Dale, Nov 22 2011 *) PROG (Haskell) a061084 n = a061084_list !! n a061084_list = 1 : 2 : zipWith (-) a061084_list (tail a061084_list) -- Reinhard Zumkeller, Feb 01 2014 (PARI) a(n)=([0, 1; 1, -1]^n*[1; 2])[1, 1] \\ Charles R Greathouse IV, Feb 09 2017 CROSSREFS Cf. A061083 for division, A000301 for multiplication and A000045 for addition - the common Fibonacci numbers. Sequence in context: A160191 A268613 A268615 * A000032 A329723 A267551 Adjacent sequences: A061081 A061082 A061083 * A061085 A061086 A061087 KEYWORD sign,easy,nice AUTHOR Ulrich Schimke (ulrschimke(AT)aol.com) EXTENSIONS Corrected by T. D. Noe, Oct 25 2006 STATUS approved

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Last modified December 5 14:51 EST 2022. Contains 358588 sequences. (Running on oeis4.)