This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A074358 Coefficient of q^1 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). 6
 0, 0, 0, 4, 20, 80, 288, 976, 3184, 10112, 31488, 96576, 292672, 878336, 2614784, 7731456, 22728448, 66482176, 193617920, 561718272, 1624101888, 4681535488, 13457924096, 38592008192, 110419341312, 315287830528, 898583560192 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Coefficient of q^0 is A002605. LINKS M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002. FORMULA G.f.: 4*x^3*(x + 1)/(2*x^2 + 2*x - 1)^2 (conjectured). - Chai Wah Wu, May 30 2016 a(n) = (1/18)*((1 + sqrt(3))^n*(-9 + 2*sqrt(3)) - (1 - sqrt(3))^n*(9 + 2*sqrt(3)) + 3*((1 - sqrt(3))^n + (1 + sqrt(3))^n)*n) for n > 0 (conjectured). - Colin Barker, Nov 17 2017 a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4) for n > 4 (conjectured). - Colin Barker, Nov 17 2017 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^1 are 0,0,0,4,20,80. MAPLE nu := proc(b, lambda, n) global q; local qp, i ; if n = 0 then RETURN(1) ; elif n =1 then RETURN(b) ; fi ; qp:=0 ; for i from 0 to n-2 do qp := qp + q^i ; od ; RETURN( b*nu(b, lambda, n-1)+lambda*qp*nu(b, lambda, n-2)) ; end: A074358 := proc(n) RETURN( coeftayl(nu(2, 2, n), q=0, 1) ) ; end: for n from 0 to 30 do printf("%d, ", A074358(n)) ; od ; # R. J. Mathar, Sep 20 2006 MATHEMATICA nu[0] = 1; nu[1] = 2; nu[n_] := nu[n] = 2*nu[n-1] + 2*Total[q^Range[0, n-2] ]*nu[n-2] // Expand; a[n_] := Coefficient[nu[n], q, 1]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Nov 17 2017 *) CROSSREFS Coefficient of q^0, q^2 and q^3 are in A002605, A074359 and A074360. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074357, A074361-A074363. Sequence in context: A303508 A258627 A082138 * A255050 A292540 A320934 Adjacent sequences:  A074355 A074356 A074357 * A074359 A074360 A074361 KEYWORD nonn AUTHOR Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002 EXTENSIONS More terms from R. J. Mathar, Sep 20 2006 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.

Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)