A289973 -id:A289973 - cp's OEIS frontend

A289974 p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S.

2, 9, 35, 139, 549, 2169, 8571, 33866, 133817, 528755, 2089288, 8255476, 32620147, 128893113, 509299806, 2012413902, 7951720511, 31419907712, 124150565816, 490560415825, 1938368302977, 7659141579267, 30263830481105, 119582517950630, 472510530626342

Offset: 0

Clark Kimberling, Aug 15 2017

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 A289780 for a guide to related sequences.

Cf. A001950, A289973.

z = 60; r = 1 + GoldenRatio; s = Sum[Floor[k*r] x^k, {k, 1, z}]; p = 1 - s;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A001950 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1]  (* A289974 *)

cp's OEIS Frontend

A289974 p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S.

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