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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). 19
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

Wikipedia, Lucas sequence

Index entries for linear recurrences with constant coefficients, signature (-1,1).

Index entries for Lucas sequences

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: A268613 A268615 A000032 * A267551 A055391 A177940

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 12 20:04 EST 2017. Contains 295954 sequences.