A289973 - OEIS

%I #8 Aug 17 2017 05:45:12

%S 1,4,11,33,96,280,818,2387,6970,20347,59401,173414,506261,1477968,

%T 4314748,12596384,36773617,107356118,313413177,914971789,2671149257,

%U 7798096555,22765597881,66461404174,194026015382,566435438933,1653639620681,4827600476829

%N p-INVERT of the lower Wythoff sequence (A000201), 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 = GoldenRatio; s = Sum[Floor[k*r] x^k, {k, 1, z}]; p = 1 - s;

%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000201 *)

%t Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1]  (* A289973 *)

%Y Cf. A000201, A289974.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Aug 15 2017