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A038608 a(n) = n*(-1)^n. 16
0, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 34, -35, 36, -37, 38, -39, 40, -41, 42, -43, 44, -45, 46, -47, 48, -49, 50, -51, 52, -53, 54, -55, 56, -57, 58, -59, 60, -61, 62, -63, 64, -65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = determinant of the (n+1) X (n+1) matrix with 0's in the main diagonal and 1's elsewhere. - Franz Vrabec, Dec 01 2007

Sum_{n>0} 1/a(n) = -log(2). - Jaume Oliver Lafont, Feb 24 2009

Pisano period lengths:  1, 2, 6, 4, 10, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, ... (is this A066043?). - R. J. Mathar, Aug 10 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (-2,-1).

FORMULA

G.f.: -x/(1+x)^2.

E.g.f: -x*exp(-x).

a(0)=0, a(1)=-1, a(n) = -2*a(n-1) - a(n-2) for n>=2. - Jaume Oliver Lafont, Feb 24 2009

MAPLE

A038608 := n->n*(-1)^n;

a:=n->sum((-1)^n, j=0..n-1): seq(a(n), n=0..73); # Zerinvary Lajos, Dec 17 2008

MATHEMATICA

lst={}; Do[AppendTo[lst, n*(-1)^n], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 18 2009 *)

PROG

(MAGMA) [n*(-1)^n: n in [0..80]]; // Vincenzo Librandi, Jun 08 2011

(PARI) a(n)=n*(-1)^n \\ Charles R Greathouse IV, Dec 07 2011

(Haskell)

a038608 n = n * (-1) ^ n

a038608_list = [0, -1] ++ map negate

   (zipWith (+) a038608_list (map (* 2) $ tail a038608_list))

-- Reinhard Zumkeller, Nov 24 2012

CROSSREFS

Cf. A002162, A155988. - Jaume Oliver Lafont, Feb 24 2009

Cf. A001477.

Sequence in context: A001489 * A105811 A209662 A272813 A258070 A258071

Adjacent sequences:  A038605 A038606 A038607 * A038609 A038610 A038611

KEYWORD

sign,easy

AUTHOR

Vasiliy Danilov (danilovv(AT)usa.net), Jul 1998

EXTENSIONS

Edited by Frank Ellermann, Jan 28 2002

STATUS

approved

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Last modified January 24 12:17 EST 2017. Contains 281237 sequences.