|
|
A289920
|
|
p-INVERT of (1,0,0,1,0,0,1,0,0,...), where p(S) = 1 - S - S^2.
|
|
1
|
|
|
1, 2, 3, 6, 12, 22, 42, 80, 151, 287, 544, 1031, 1956, 3708, 7031, 13333, 25280, 47936, 90895, 172350, 326806, 619677, 1175008, 2228011, 4224672, 8010672, 15189552, 28801880, 54613096, 103555397, 196358029, 372327066, 705993241, 1338679088, 2538355336
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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 A291728 for a guide to related sequences.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -((-1 - x + x^3)/(1 - x - x^2 - 2 x^3 + x^4 + x^6)).
a(n) = a(n-1) + a(n-2) + 2*a(n-3) - a(n-4) - a(n-6) for n >= 7.
|
|
MATHEMATICA
|
z = 60; s = x/(x - x^3); p = 1 - s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A079978 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A289920 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|