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A052981
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Expansion of ( 1-x ) / ( 1-4*x-3*x^2+3*x^3 ).
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1
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1, 3, 15, 66, 300, 1353, 6114, 27615, 124743, 563475, 2545284, 11497332, 51934755, 234595164, 1059692925, 4786752927, 21622304991, 97670399970, 441188256072, 1992897309225, 9002142805206, 40663698380283, 183682530009075, 829714786761531, 3747915641932500
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-x)/(1-4*x-3*x^2+3*x^3).
Recurrence: {a(0)=1, a(1)=3, a(2)=15, 3*a(n)-3*a(n+1)-4*a(n+2)+a(n+3)=0}.
Sum(-1/95*(-11-22*r+15*r^2)*r^(-1-n) where r=RootOf(1-4*_Z-3*_Z^2+3*_Z^3)).
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MAPLE
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spec:= [S, {S=Sequence(Prod(Union(Z, Z, Z), Union(Sequence(Z), Z)))}, unlabeled]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
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PROG
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(Magma) I:=[1, 3, 15]; [n le 3 select I[n] else 4*Self(n-1)+3*Self(n-2) -3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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