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

2, 13, 71, 376, 1991, 10564, 56051, 297384, 1577797, 8371133, 44413759, 235640987, 1250213362, 6633113651, 35192550325, 186717077925, 990643385291, 5255942989944, 27885853904294, 147950776760552, 784965467407868, 4164701250741605, 22096177765889378

Offset: 0

Author

Clark Kimberling, Aug 14 2017

Keywords

• nonn
• easy

Comments

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.

Crossrefs

Cf. A001950, A289925.

Programs

Mathematica

z = 60; r = 1 + GoldenRatio; s = Sum[Floor[k*r] x^k, {k, 1, z}]; p = 1 - s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A001950 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1]  (* A289926 *)