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A074362
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).
2
0, 0, 0, 0, 10, 66, 336, 1527, 6513, 26667, 106102, 413265, 1583331, 5986689, 22392606, 83002842, 305308666, 1115587020, 4052786850, 14648359515, 52705460583, 188868467853, 674332868566, 2399653030899, 8513523719661
OFFSET
0,5
COMMENTS
Coefficient of q^0 is A006190(n+1).
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.: (-3*x^7 - 18*x^6 - 24*x^5 + 10*x^4)/(1 - 3*x - x^2)^3.
EXAMPLE
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.
MATHEMATICA
Join[{0, 0}, LinearRecurrence[{9, -24, 9, 24, 9, 1}, {0, 0, 10, 66, 336, 1527}, 30]] (* Jean-François Alcover, Dec 13 2018 *)
CROSSREFS
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.
Sequence in context: A211056 A269468 A024391 * A080421 A320817 A004310
KEYWORD
nonn
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
EXTENSIONS
More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002
STATUS
approved