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A136305
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Expansion of g.f. (3 -x +2*x^2)/(1 -3*x +2*x^2 -x^3).
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9
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3, 8, 20, 47, 109, 253, 588, 1367, 3178, 7388, 17175, 39927, 92819, 215778, 501623, 1166132, 2710928, 6302143, 14650705, 34058757, 79177004, 184064203, 427897358, 994740672, 2312491503, 5375890523, 12497429235, 29052998162, 67540026539, 157011512528
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OFFSET
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0,1
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COMMENTS
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Previous name: Transform of A000027 by the T_{1,2} transformation (see link).
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LINKS
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FORMULA
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G.f.: f(z) = 3 +8*z + ... = (3 -z +2*z^2)/(1 -3*z +2*z^2 -z^3).
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MATHEMATICA
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LinearRecurrence[{3, -2, 1}, {3, 8, 20}, 40] (* G. C. Greubel, Apr 19 2021 *)
CoefficientList[Series[(3-x+2x^2)/(1-3x+2x^2-x^3), {x, 0, 40}], x] (* Harvey P. Dale, Oct 15 2021 *)
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PROG
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(Magma) [n le 3 select 2^(n-1)*(n+2) else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): n in [1..41]]; // G. C. Greubel, Apr 19 2021
(Sage)
@CachedFunction
def a(n): return 2^n*(n+3) if n<3 else sum((-1)^j*(3-j)*a(n-j-1) for j in (0..2))
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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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STATUS
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approved
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