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).
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7, -11)
FORMULA
G.f.: (1 - 2 x)/(1 - 7 x + 11 x^2).
a(n) = 7*a(n-1) - 11*a(n-2).
a(n) = (2^(-n-1)*((7-sqrt(5))^(n+1)*(-4+sqrt(5)) + (4+sqrt(5))*(7+sqrt(5))^(n+1))) / (11*sqrt(5)). - Colin Barker, Aug 11 2017
MATHEMATICA
PROG
(PARI) Vec(x*(1 - 2*x) / (1 - 7*x + 11*x^2) + O(x^30)) \\ Colin Barker, Aug 11 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Aug 10 2017
STATUS
approved