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A074363
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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).
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11
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0, 0, 0, 0, 36, 246, 1293, 6057, 26592, 111934, 457353, 1827529, 7176636, 27789976, 106371588, 403204880, 1515647250, 5656172420, 20974163475, 77339044883, 283743384228, 1036296662574, 3769287797151, 13658724680991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Coefficient of q^0 is A006190(n+1).
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REFERENCES
| Paper in progress by Y. Kelly Itakura, to appear.
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LINKS
| M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, Lifting of Nichols Algebras of Type $B_2$
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FORMULA
| G.f. has denominator (1-3x-x^2)^4.
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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.
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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: A166329 A159921 A129149 * A030165 A017342 A115332
Adjacent sequences: A074360 A074361 A074362 * A074364 A074365 A074366
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KEYWORD
| nonn
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AUTHOR
| Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
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EXTENSIONS
| More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002
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