0,4

Apart from signs, generated by 1,1 position of H_2^n=[1,1;-1,1]^n; and a(n)=2^(n/2)cos(pi*n/2) - Paul Barry (pbarry(AT)wit.ie), Feb 18 2004

Equals binomial transform of [1, 0, -1, 0, 1, 0, -1, 0,...]; (an infinitely periodic sequence with a 4-cycle of [1, 0, -1, 0,...]). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 25 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Real part of (-1-i)^n - Marc LeBrun (mlb(AT)well.com)

a(n)=-2*(a(n-1)+a(n-2)), a(0)=1, a(1)=-1 - Michael Somos

Sum_{j=0..[n/2]} (-1)^j*binomial(n, 2*j).

G.f.: (1+x)/(1+2x+2x^2). E.g.f.: cos(x)/exp(x).

a(n)= Sum_{k, 0<=k<=n}(-1)^k*A098158(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2006

a(n)*(-1)^n=A099087(n)-A099087(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007

a(n)=1/2*[(-1-I)^n+(-1+I)^n], with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 21 2008]

a(n)=(-1)^n*A146559(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]

A009116 := n->add((-1)^j*binomial(n, 2*j), j=0..floor(n/2));

Cos[ x ]/Exp[ x ]

(PARI) a(n)=if(n<0, 0, polcoeff((1+x)/(1+2*x+2*x^2)+x*O(x^n), n))

Cf. A009545.

Cf. A090132.

(With different signs) Row sums of triangle A104597.

Sequence in context: A163089 A111172 A112793 this_sequence A146559 A118434 A090132

Adjacent sequences: A009113 A009114 A009115 this_sequence A009117 A009118 A009119

sign,easy,nice

R. H. Hardin (rhhardin(AT)att.net)

Extended with signs Mar 15 1997 by Olivier Gerard.