A289974 -id:A289974 - cp's OEIS frontend

A289973 p-INVERT of the lower Wythoff sequence (A000201), where p(S) = 1 - S.

1, 4, 11, 33, 96, 280, 818, 2387, 6970, 20347, 59401, 173414, 506261, 1477968, 4314748, 12596384, 36773617, 107356118, 313413177, 914971789, 2671149257, 7798096555, 22765597881, 66461404174, 194026015382, 566435438933, 1653639620681, 4827600476829

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. A000201, A289974.

z = 60; r = GoldenRatio; s = Sum[Floor[k*r] x^k, {k, 1, z}]; p = 1 - s;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000201 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1]  (* A289973 *)

cp's OEIS Frontend

A289973 p-INVERT of the lower Wythoff sequence (A000201), where p(S) = 1 - S.

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