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A289926 p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S - S^2. 3

%I

%S 2,13,71,376,1991,10564,56051,297384,1577797,8371133,44413759,

%T 235640987,1250213362,6633113651,35192550325,186717077925,

%U 990643385291,5255942989944,27885853904294,147950776760552,784965467407868,4164701250741605,22096177765889378

%N p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S - S^2.

%C 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).

%C See A289780 for a guide to related sequences.

%t z = 60; r = 1 + GoldenRatio; s = Sum[Floor[k*r] x^k, {k, 1, z}]; p = 1 - s - s^2;

%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A001950 *)

%t Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1] (* A289926 *)

%Y Cf. A001950, A289925.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Aug 14 2017

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Last modified May 23 04:59 EDT 2019. Contains 323508 sequences. (Running on oeis4.)