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A291416
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p-INVERT of (1,1,0,0,0,0,...), where p(S) = 1 - 4 S + S^2.
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2
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4, 19, 86, 392, 1784, 8121, 36966, 168267, 765940, 3486508, 15870352, 72240785, 328835240, 1496836103, 6813498210, 31014589884, 141176346720, 642625324009, 2925187658218, 13315259321575, 60610173266216, 275893470389144, 1255848695053856, 5716539585528849
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OFFSET
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0,1
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COMMENTS
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Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the "INVERT" transform of s, so that p-INVERT is a generalization of the "INVERT" transform (e.g., A033453).
See A291382 for a guide to related sequences.
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LINKS
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FORMULA
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G.f.: -(((1 + x) (-4 + x + x^2))/(1 - 4 x - 3 x^2 + 2 x^3 + x^4)).
a(n) = 4*a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n >= 5.
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MATHEMATICA
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z = 60; s = x + x^2; p = 1 - 4 s + s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A019590 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291416 *)
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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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