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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074359 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(2,2). 3
0, 0, 0, 0, 12, 64, 280, 1088, 3968, 13856, 46912, 155136, 503616, 1610496, 5086336, 15895552, 49229312, 151275008, 461662208, 1400356864, 4224703488, 12683452416, 37911164928, 112865394688, 334788444160, 989756825600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Coefficient of q^0 is A002605.

LINKS

Table of n, a(n) for n=0..25.

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

Index entries for linear recurrences with constant coefficients, signature (6, -6, -16, 12, 24, 8).

FORMULA

Conjecture: O.g.f: 4*x^4*(-3+2*x+8*x^2+4*x^3)/(2*x^2+2*x-1)^3. - R. J. Mathar, Jul 22 2009

EXAMPLE

The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=6, nu(3)=16+4q, nu(4)=44+20q+12q^2, nu(5)=120+80q+64q^2+40q^3+8q^4, so the coefficients of q^2 are 0,0,0,0,12,64.

MAPLE

nu := proc(n, b, lambda) if n = 0 then 1 ; elif n = 1 then b ; else b*nu(n-1, b, lambda)+lambda*nu(n-2, b, lambda)*add(q^i, i=0..n-2) ; fi ; end: A074359 := proc(n) local b, lambda, thisnu ; b := 2 ; lambda := 2 ; thisnu := nu(n, b, lambda) ; RETURN( coeftayl(thisnu, q=0, 2) ) ; end: for n from 0 to 40 do printf("%d, ", A074359(n) ) ; od ; # R. J. Mathar, Mar 20 2007

MATHEMATICA

Join[{0, 0}, LinearRecurrence[{6, -6, -16, 12, 24, 8}, {0, 0, 12, 64, 280, 1088}, 24]] (* Jean-François Alcover, Sep 23 2017 *)

CROSSREFS

Coefficient of q^0, q^1 and q^3 are in A002605, A074358 and A074360. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074357, A074361-A074363.

Sequence in context: A105916 A193872 A258617 * A104062 A232383 A003868

Adjacent sequences:  A074356 A074357 A074358 * A074360 A074361 A074362

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from R. J. Mathar, Mar 20 2007

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 23:27 EST 2018. Contains 317221 sequences. (Running on oeis4.)