|
%I #6 Aug 15 2017 19:28:52
%S 1,5,19,72,265,979,3618,13374,49447,182807,675843,2498594,9237316,
%T 34150422,126254366,466763346,1725627604,6379658213,23585644300,
%U 87196304028,322365390600,1191787269208,4406046481612,16289186920873,60221246337260,222638399818776
%N p-INVERT of the lower Wythoff sequence (A000201), where p(S) = 1 - S - S^2.
%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 - s^2;
%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000201 *)
%t Drop[CoefficientList[Series[1/p, {x, 0, z}], x] , 1] (* A289925 *)
%Y Cf. A000201, A289926.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Aug 14 2017
|
