A074353 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)=(1,2).

0, 0, 0, 0, 6, 20, 70, 196, 542, 1396, 3526, 8628, 20766, 49092, 114598, 264356, 603998, 1368148, 3076166, 6870740, 15256158, 33696804, 74073510, 162127940, 353460766, 767816500, 1662394310, 3588252916, 7723318942, 16580031876, 35506388646, 75864499428

Offset

0,5

Comments

Coefficient of q^0 is A001045(n+1).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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 (3,3,-11,-6,12,8).

Formula

a(0)=0 for n>0, a(n) = (1/81)*(2^(n-1)*(6*n^2-43) + (-1)^n*(6*n^2-24*n+62)). - Benoit Cloitre, Jan 16 2003

From Colin Barker, Nov 18 2017: (Start)

G.f.: 2*x^4*(3 + x - 4*x^2 - 4*x^3) / ((1 + x)^3*(1 - 2*x)^3).

a(n) = 3*a(n-1) + 3*a(n-2) - 11*a(n-3) - 6*a(n-4) + 12*a(n-5) + 8*a(n-6) for n>7.

(End)

Example

The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=3, nu(3)=5+2q, nu(4)=11+8q+6q^2, nu(5)=21+22q+20q^2+14q^3+4q^4, so the coefficients of q^2 are 0,0,0,0,6,20.

Prog

(PARI) concat(vector(4), Vec(2*x^4*(3 + x - 4*x^2 - 4*x^3) / ((1 + x)^3*(1 - 2*x)^3) + O(x^40))) \\ Colin Barker, Nov 18 2017

Crossrefs

Coefficients of q^0, q^1 and q^3 are in A001045, A074352 and A074354. Related sequences with other values of b and lambda are in A074082-A074089, A074355-A074363.

Sequence in context: A318337 A264307 A050930 * A075055 A146891 A235367

Adjacent sequences: A074350 A074351 A074352 * A074354 A074355 A074356

Keyword

nonn,easy

Author

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

Extensions

More terms from Benoit Cloitre, Jan 16 2003

Corrected by T. D. Noe, Oct 25 2006

Status

approved