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A074361
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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).
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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.: (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) [From Harvey P. Dale, Jan 16 2012]
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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 0,0,0,3,19,93.
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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]] (* From Harvey P. Dale, Jan 16 2012 *)
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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.
Sequence in context: A183384 A050863 A049153 * A126187 A198763 A047029
Adjacent sequences: A074358 A074359 A074360 * A074362 A074363 A074364
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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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