Sequence needed for shortest path

[David Wilson]

At the moment, it is conjectured that the shortest path is of length
a(n) = 2*ceil(n/sqrt(2)), if not, the first departure is beyond n = 10000.
Probably the best thing to do is add a sequence for 2*ceil(n/sqrt(2))
and note the conjecture:

%I A000001
%S A000001 
0,2,4,6,6,8,10,10,12,14,16,16,18,20,20,22,24,26,26,28,30,30,32,34,34,36,
%T A000001 
38,40,40,42,44,44,46,48,50,50,52,54,54,56,58,58,60,62,64,64,66,68,68,70,
%U A000001 
72,74,74,76,78,78,80,82,84,84,86,88,88,90,92,92,94,96,98,98,100,102,102
%N A000001 2*ceil(n/sqrt(2))
%O A000001 0,2
%C A000001 Conjecturally, length of shortest polygonal path from (0,0) to 
(n,n) with integer vertices and edges.  Holds for n <= 10000.
%F A000001 a(n) = 2*A049474(n).
%K A000001 nonn,easy

- David W. Wilson

"Truth is just truth -- You can't have opinions about the truth."
   - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"