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A129080
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Expansion of g.f. x*(x^4 - 5*x^3 + 10*x^2 - 12*x + 4)/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)).
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1
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4, 8, 14, 25, 48, 99, 215, 482, 1100, 2534, 5865, 13606, 31599, 73425, 170656, 396688, 922146, 2143685, 4983416, 11584987, 26931775, 62608726, 145547572, 338356994, 786584517, 1828587086, 4250949167, 9882257793, 22973462076, 53406819752, 124155792838
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: x*(x^4 - 5*x^3 + 10*x^2 - 12*x + 4)/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; corrected by R. J. Mathar, Sep 16 2009]
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MAPLE
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m:=40; S:=series( x*(x^4-5*x^3+10*x^2-12*x+4)/((1-x)^2*(1-3*x+2*x^2-x^3)), x, m+1):
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MATHEMATICA
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b[n_]:= b[n]= If[n<4, 2^n -1, 3*b[n-1] -2*b[n-2] +b[n-3]];
a[n_]:= a[n]= If[n==1, 4, a[n-1] +b[n] -b[n-1] +2];
LinearRecurrence[{5, -9, 8, -4, 1}, {4, 8, 14, 25, 48}, 40] (* Harvey P. Dale, Feb 14 2015 *)
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PROG
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(Magma)
b:= func< n | n lt 4 select 2^n -1 else 3*Self(n-1) -2*Self(n-2) +Self(n-3) >;
(Sage)
@CachedFunction
def b(n): return 2^n -1 if n < 4 else 3*b(n-1) -2*b(n-2) +b(n-3)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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New name using Maksym Voznyy's g.f., Joerg Arndt, Apr 13 2021
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STATUS
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approved
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