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%I #7 Aug 19 2017 13:22:03
%S 2,9,35,139,549,2169,8571,33866,133817,528755,2089288,8255476,
%T 32620147,128893113,509299806,2012413902,7951720511,31419907712,
%U 124150565816,490560415825,1938368302977,7659141579267,30263830481105,119582517950630,472510530626342
%N p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S.
%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;
%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A001950 *)
%t Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1] (* A289974 *)
%Y Cf. A001950, A289973.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Aug 15 2017
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