A074361 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)=(3,1).

0, 0, 0, 3, 19, 93, 407, 1674, 6618, 25455, 95953, 356151, 1305887, 4741092, 17072484, 61055787, 217074895, 767882865, 2704365719, 9487509102, 33170122494, 115614094071, 401864286637, 1393378817259, 4820368210175

Offset: 0

Author

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

Keywords

• nonn

Comments

Coefficient of q^0 is A006190(n+1).

Examples

			The first 6 nu polynomials are nu(0)=1, nu(1)=3, nu(2)=10, nu(3)=33+3q, nu(4)=109+19q+10q^2, nu(5)=360+93q+66q^2+36q^3+3q^4, so the coefficients of q^1 are 0,0,0,3,19,93.
		

Links

• 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, -7, -6, -1).

Crossrefs

Coefficient of q^0, q^2 and q^3 are in A006190, A074362 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.

Programs

Mathematica

CoefficientList[Series[(x^4+3x^3)/(1-3x-x^2)^2,{x,0,30}],x] (* or *) Join[{0},LinearRecurrence[{6,-7,-6,-1},{0,0,3,19},30]] (* Harvey P. Dale, Jan 16 2012 *)

Formula

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

a(0)=0, a(1)=0, a(2)=0, a(3)=3, a(4)=19, a(n)=6*a(n-1)-7*a(n-2)- 6*a(n-3)- a(n-4). - Harvey P. Dale, Jan 16 2012

Extensions

More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002