login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072996 Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=b*nu(n-1)+lambda*(n-1)_q*nu(n-2) with (b,lambda)=(2,1), where (n)_q=(1+q+...+q^(n-1)) and q is a root of unity. 0
1, 1, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Instead of listing the coefficients of the highest power of q in each nu(n), if we list the coefficients of the smallest power of q (i.e., constant terms), we get a weighted Fibonacci numbers described by f(0)=1, f(1)=1, for n>=2, f(n)=2f(n-1)+f(n-2).

LINKS

Table of n, a(n) for n=0..104.

M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.

FORMULA

For given b and lambda, the recurrence relation is given by; t(0)=1, t(1)=b, t(2)=b^2+lambda and for n>=3, t(n)=lambda*t(n-2).

O.g.f.: -(x+1+4*x^2)/((x-1)*(x+1)) = -4-3/(x-1)+2/(x+1). - R. J. Mathar, Dec 05 2007

EXAMPLE

nu(0)=1, nu(1)=2, nu(2)=5, nu(3)=12+2q, nu(4)=29+9q+5q^2, nu(5)=70+32q+24q^2+14q^3+2q^4, nu(6)=169+102q+91q^2+42q^3+38q^4+9q^5+5q^6. By listing the coefficients of the highest power in each nu(n) we get 1,2,5,2,5,2,5,...

CROSSREFS

Cf. A000129.

Sequence in context: A111129 A168464 A059688 * A244892 A278066 A153107

Adjacent sequences:  A072993 A072994 A072995 * A072997 A072998 A072999

KEYWORD

nonn

AUTHOR

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

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 August 3 19:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)