OFFSET
1,2
COMMENTS
Let S be the sequence (or tree) of complex numbers defined by these rules: 0 is in S, and if x is in S, then x + 1, and i*x are in S. Deleting duplicates as they occur, the generations of S are given by g(1) = (0), g(2) = (1), g(3) = (2,i), g(4) = (3, 2i, 1+i, -1), ... Concatenating these gives 0, 1, 2, i, 3, 2*i, 1 + i, -1, 4, 3*i, 1 + 2*i, -2, 2 + i, -1 + i, -i, 5, ... A232868 is the (ordered) union of two linearly recurrent sequences: A232866 and A232867.
FORMULA
From Chai Wah Wu, Feb 20 2018: (Start)
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 10 (conjectured).
G.f.: x*(-x^9 - 4*x^7 + 2*x^6 + 2*x^5 - 2*x^4 + x^2 - x - 1)/((x - 1)^3*(x + 1)^2) (conjectured). (End)
EXAMPLE
Each x begets x + 1, and i*x, but if either these has already occurred it is deleted. Thus, 0 begets (1); then 1 begets (2,i,); then 2 begets 3 and 2*i, and i begets 1 + i and -1, so that g(4) = (3, 2*i, 1 + i, -1), etc.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 01 2013
STATUS
approved