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A053297
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Row sums of array T in A053199.
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1
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1, 5, 22, 92, 372, 1468, 5688, 21728, 82064, 307088, 1140320, 4206912, 15434048, 56350912, 204875648, 742104064, 2679197952, 9644109056, 34623075840, 124001176576, 443136848896, 1580464036864, 5626501838848, 19996918849536
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OFFSET
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1,2
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COMMENTS
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The generating series is a power series composition G(F(t)) where
F(t) = t + 3*t^2 + 7*t^3 + 15*t^4 + ... is generating series of A000225,
and G(t) = t + 2*t^2 + 3*t^3 + 4*t^4 + ... is generating series of the
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LINKS
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FORMULA
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G.f.: x * (1 - x) * (1 - 2*x) / (1 - 4*x + 2*x^2)^2. - Michael Somos, Nov 03 2016
a(n) = 8*a(n-1) + 20*a(n-2) - 16*a(n-3) + 4*a(n-4) for all n in Z. - Michael Somos, Nov 03 2016
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EXAMPLE
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G.f. = x + 5*x^2 + 22*x^3 + 92*x^4 + 372*x^5 + 1468*x^6 + 5688*x^7 + 21728*x^8 + ...
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MATHEMATICA
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Drop[CoefficientList[Series[x*(1-x)*(1-2*x)/(1-4*x+2*x^2)^2, {x, 0, 50}], x], 1] (* G. C. Greubel, May 24 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(x*(1-x)*(1-2*x)/(1-4*x+2*x^2)^2) \\ G. C. Greubel, May 24 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x)*(1-2*x)/(1-4*x+2*x^2)^2)); // G. C. Greubel, May 24 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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