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 A292480 for a guide to related sequences.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7, -19, 23, -8, 6)
FORMULA
G.f.: -(((1 + x) (1 - 5 x + 8 x^2 - x^3 + x^4))/((-1 + 3 x) (1 - 4 x + 7 x^2 - 2 x^3 + 2 x^4))).
a(n) = 7*a(n-1) - 19*a(n-2) + 23*a(n-3) - 8*a(n-4) + 6*a(n-5) for n >= 7.
MATHEMATICA
PROG
(PARI) x='x+O('x^99); Vec(((1+x)*(1-5*x+8*x^2-x^3+x^4))/((1-3*x)*(1-4*x+7*x^2-2*x^3+2*x^4))) \\ Altug Alkan, Oct 03 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 03 2017
STATUS
approved