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A074363 Coefficient of q^3 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). 12
0, 0, 0, 0, 36, 246, 1293, 6057, 26592, 111934, 457353, 1827529, 7176636, 27789976, 106371588, 403204880, 1515647250, 5656172420, 20974163475, 77339044883, 283743384228, 1036296662574, 3769287797151, 13658724680991, 49325767966842, 177570110818794 (list; graph; refs; listen; history; text; internal format)
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.
Index entries for linear recurrences with constant coefficients, signature (12,-50,72,21,-72,-50,-12,-1).
FORMULA
From Colin Barker, Nov 18 2017: (Start)
G.f.: x^4*(3 + x)*(12 - 66*x + 69*x^2 + 60*x^3 + 10*x^4) / (1 - 3*x - x^2)^4.
a(n) = 12*a(n-1) - 50*a(n-2) + 72*a(n-3) + 21*a(n-4) - 72*a(n-5) - 50*a(n-6) - 12*a(n-7) - a(n-8) for n>9.
(End)
EXAMPLE
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 0,0,0,0,0,36.
PROG
(PARI) concat(vector(4), Vec(x^4*(3 + x)*(12 - 66*x + 69*x^2 + 60*x^3 + 10*x^4) / (1 - 3*x - x^2)^4 + O(x^40))) \\ Colin Barker, Nov 18 2017
CROSSREFS
Coefficients of q^0, q^1 and q^2 are in A006190, A074361 and A074362. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.
Sequence in context: A326347 A129149 A223558 * A219888 A233363 A030165
KEYWORD
nonn,easy
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

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)