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A075193 Expansion of (1-2*x)/(1+x-x^2). 5
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, -87403803, 141422324 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

"Inverted" Lucas numbers:

The g.f. is obtained inserting 1/x into the g.f. of Lucas sequence and dividing by x. The closed form is a(n)=(-1)^n*a^(n+1)+(-1)^n*b^(n+1), where a=golden ratio and b=1-a, so that a(n)=(-1)^n*L(n+1), L(n)=Lucas numbers.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = -a(n-1)+a(n-2), a(0)=1, a(1)=-3.

a(n) = term (1,1) in the 1x2 matrix [1,-2] * [-1,1; 1,0]^n. - Alois P. Heinz, Jul 31 2008

a(n) = A186679(n)+A186679(n-2) for n>1. - Reinhard Zumkeller, Feb 25 2011

a(n) = A039834(n+1)-2*A039834(n). - R. J. Mathar, Sep 27 2014

MAPLE

a:= n-> (Matrix([[1, -2]]). Matrix([[-1, 1], [1, 0]])^(n))[1, 1]:

seq(a(n), n=0..45); # Alois P. Heinz, Jul 31 2008

MATHEMATICA

CoefficientList[Series[(1 - 2z)/(1 + z - z^2), {z, 0, 40}], z]

PROG

(Haskell)

a075193 n = a075193_list !! n

a075193_list = 1 : -3 : zipWith (-) a075193_list (tail a075193_list)

-- Reinhard Zumkeller, Sep 15 2015

CROSSREFS

Cf. A000032.

Sequence in context: A093090 A193686 A000204 * A042433 A024319 A041209

Adjacent sequences:  A075190 A075191 A075192 * A075194 A075195 A075196

KEYWORD

easy,sign

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Sep 07 2002

STATUS

approved

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Last modified March 24 07:54 EDT 2017. Contains 283985 sequences.