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%I #19 Mar 03 2024 11:38:51
%S 0,0,0,0,10,66,336,1527,6513,26667,106102,413265,1583331,5986689,
%T 22392606,83002842,305308666,1115587020,4052786850,14648359515,
%U 52705460583,188868467853,674332868566,2399653030899,8513523719661
%N 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) = (3,1).
%C Coefficient of q^0 is A006190(n+1).
%H M. Beattie, S. Dăscălescu and S. Raianu, <a href="https://arxiv.org/abs/math/0204075">Lifting of Nichols Algebras of Type B_2</a>, arXiv:math/0204075 [math.QA], 2002.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9, -24, 9, 24, 9, 1).
%F G.f.: (-3*x^7 - 18*x^6 - 24*x^5 + 10*x^4)/(1 - 3*x - x^2)^3.
%e The first 6 nu polynomials are nu(0) = 1, nu(1) = 3, nu(2) = 10, nu(3) = 33 + 3*q, nu(4) = 109 + 19*q + 10*q^2, nu(5) = 360 + 93*q + 66*q^2 + 36*q^3 + 3*q^4, so the coefficients of q^1 are 0,0,0,0,10,66.
%t Join[{0, 0}, LinearRecurrence[{9, -24, 9, 24, 9, 1}, {0, 0, 10, 66, 336, 1527}, 30]] (* _Jean-François Alcover_, Dec 13 2018 *)
%Y Coefficient of q^0, q^1 and q^3 are in A006190, A074361 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.
%K nonn
%O 0,5
%A Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
%E More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002