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A291415
p-INVERT of (1,1,0,0,0,0,...), where p(S) = 1 - 3 S + S^2.
2
3, 11, 37, 126, 427, 1448, 4909, 16643, 56424, 191292, 648529, 2198680, 7454090, 25271280, 85676131, 290464093, 984747891, 3338548317, 11318536416, 38372746007, 130093466328, 441050269849, 1495273713773, 5069362002354, 17186439428582, 58266444593059
OFFSET
0,1
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 A291382 for a guide to related sequences.
FORMULA
G.f.: -(((1 + x) (-3 + x + x^2))/(1 - 3 x - 2 x^2 + 2 x^3 + x^4)).
a(n) = 3*a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) for n >= 5.
MATHEMATICA
z = 60; s = x + x^2; p = 1 - 3 s + s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A019590 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291415 *)
CROSSREFS
Sequence in context: A192339 A027064 A027066 * A046722 A214996 A180168
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 07 2017
STATUS
approved