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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074085 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)=(2,1). 2
0, 0, 0, 0, 5, 24, 91, 308, 978, 2978, 8802, 25440, 72251, 202316, 559941, 1534548, 4170256, 11250630, 30158900, 80389600, 213204513, 562896832, 1480086111, 3877337556, 10123000126, 26347306474, 68378847990, 176994780672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The coefficient of q^0 is the Pell number A000129(n+1).

REFERENCES

Paper in progress by Y. Kelly Itakura, to appear.

LINKS

Table of n, a(n) for n=0..27.

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

FORMULA

G.f.: (5x^4-6x^5-8x^6-2x^7)/(1-2x-x^2)^3.

a(n)=6a(n-1)-9a(n-2)-4a(n-3)+9a(n-4)+6a(n-5)+a(n-6) for n>=8.

EXAMPLE

The first 6 nu polynomials are 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, so the coefficients of q^2 are 0,0,0,0,5,24.

MATHEMATICA

b=2; lambda=1; expon=2; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]

CROSSREFS

Coefficients of q^0, q^1 and q^3 are in A000129, A074084 and A074086. Related sequences with other values of b and lambda are in A074082-A074083 and A074087-A074089.

Sequence in context: A220316 A220339 A158499 * A145914 A066316 A271458

Adjacent sequences:  A074082 A074083 A074084 * A074086 A074087 A074088

KEYWORD

nonn

AUTHOR

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002

EXTENSIONS

Edited by Dean Hickerson, 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 04:45 EST 2016. Contains 278960 sequences.