login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A104537 Expansion of g.f.: (1+x)/(1+2*x+4x^2). 4
1, -1, -2, 8, -8, -16, 64, -64, -128, 512, -512, -1024, 4096, -4096, -8192, 32768, -32768, -65536, 262144, -262144, -524288, 2097152, -2097152, -4194304, 16777216, -16777216, -33554432, 134217728, -134217728, -268435456, 1073741824, -1073741824, -2147483648, 8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1) is the Hankel transform of C(2n,n)-C(2n+2,n+1). - Paul Barry, Mar 14 2008

a(n+1) is the Hankel transform of C(2n,n)-2*C(n)=((n-1)/(n+1))*C(2n,n), where C(n)=A000108(n). - Paul Barry, Mar 14 2008

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (-2,-4).

FORMULA

G.f.: (1+x)/(1+2*x+4x^2).

a(n) = -2*a(n-1) - 4*a(n-2).

a(n) = 2^n*cos(2*Pi*n/3).

a(n) = Sum_{k, 0<=k<=n} A098158(n,k)*(-1)^k*3^(n-k). - Philippe Deléham, Nov 14 2008

a(n) = (1/2)*{[ -1+I*sqrt(3)]^n+[ -1-I*sqrt(3)]^n}, with n>=0. - Paolo P. Lava, Nov 19 2008

a(n) = 3^n/2^n*product(i=1,n,1/3-tan((i-1/2)*Pi/(2*n))^2). - Gerry Martens, May 26 2011

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(3*k+1)/(x*(3*k+4) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 26 2013

a(n) = b(n)+b(n-1) where b(n) = 2^n*A049347(n). - R. J. Mathar, May 21 2019

MAPLE

A104537:=n->2^n*cos(2*Pi*n/3): seq(A104537(n), n=0..40); # Wesley Ivan Hurt, Nov 16 2014

MATHEMATICA

CoefficientList[Series[(1 + x) / (1 + 2 x + 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 16 2014 *)

LinearRecurrence[{-2, -4}, {1, -1}, 40] (* Harvey P. Dale, Dec 02 2019 *)

PROG

(MAGMA) I:=[1, -1]; [n le 2 select I[n] else -2*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Nov 16 2014

CROSSREFS

Cf. A000108, A098158.

Sequence in context: A290378 A138230 A128018 * A019240 A269510 A093907

Adjacent sequences:  A104534 A104535 A104536 * A104538 A104539 A104540

KEYWORD

easy,sign,changed

AUTHOR

Paul Barry, Mar 13 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)