OFFSET
0,2
COMMENTS
From Charlie Neder, Feb 06 2019: (Start)
Colin Barker's conjectures below are true.
Proof: A267181(ka,kb) = A267181(a,b) since both operations preserve the greatest common factor of the two coordinates, so A267181(2k,2) = A267181(k,1) = k for k > 1, the second conjecture. For odd coordinates, we have the forced chain (2k+1,2) -> (2,2k+1) -> (2,2k-1) -> ... -> (2,1) -> (1,2) -> (1,1) with k+3 operations, the third conjecture. The rest follow from combining these. (End)
FORMULA
Conjectures from Colin Barker, Jan 29 2016: (Start)
a(n) = (1-5*(-1)^n+2*n)/4 for n>0.
a(n) = (n-2)/2 for n>0 and even.
a(n) = (n+3)/2 for n odd.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)).
(End) [These are true - see Comments]
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 17 2016
STATUS
approved