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A137249
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Expansion of g.f. z*(2-2*z+z^2+z^3)/((1+z)*(1-3*z+2*z^2-z^3)).
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6
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2, 2, 7, 15, 37, 84, 197, 456, 1062, 2467, 5737, 13335, 31002, 72069, 167542, 389486, 905447, 2104907, 4893317, 11375580, 26445017, 61477204, 142917162, 332242091, 772369157, 1795540447, 4174125122, 9703663625, 22558281082
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OFFSET
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1,1
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COMMENTS
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Previous name was: Transform of A033999 by the T_{0,1} transformation (see link).
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LINKS
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FORMULA
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O.g.f: z*(2 -2*z +z^2 +z^3)/( (1+z)*(1-3*z+2*z^2-z^3) ).
a(n+4) = 2*a(n+3) + a(n+2) - a(n+1) + a(n).
a(n) = (1/7)*( 4*(-1)^n + Sum_{j=0..floor(n/2)} ( 10*binomial(n+j+2, 3*j+2) - 12*binomial(n+j+1, 3*j+2) + 11*binomial(n+j, 3*j+2) ) ). (End)
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MAPLE
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m:= 40;
S:= series( x*(2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)), x, m+1);
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MATHEMATICA
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LinearRecurrence[{2, 1, -1, 1}, {2, 2, 7, 15}, 30] (* Harvey P. Dale, Feb 02 2012 *)
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PROG
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(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)) )); // G. C. Greubel, Apr 11 2021
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)) ).list()
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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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EXTENSIONS
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STATUS
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approved
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