OFFSET
0,2
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.
FORMULA
Conjectures from Colin Barker, Aug 15 2017: (Start)
G.f.: (1 - x^2 + x^3)*(1 + x - x^3) / (1 - 3*x - 4*x^2 + 7*x^3 + 5*x^4 - 7*x^5 - 4*x^6 + 3*x^7 + x^8).
a(n) = 3*a(n-1) + 4*a(n-2) - 7*a(n-3) - 5*a(n-4) + 7*a(n-5) + 4*a(n-6) - 3*a(n-7) - a(n-8) for n>7.
(End)
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 14 2017
STATUS
approved