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A322042 Maximum edge-distance of a point in the quotient graph E/nE from the origin (see A322041 for further information). 2

%I

%S 0,1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,14,15,16,16,17,18,

%T 18,19,20,20,21,22,22,23,24,24,25,26,26,27,28,28,29,30,30,31,32,32,33,

%U 34,34,35,36,36,37,38,38,39,40,40,41,42,42

%N Maximum edge-distance of a point in the quotient graph E/nE from the origin (see A322041 for further information).

%H N. J. A. Sloane, <a href="/A322042/b322042.txt">Table of n, a(n) for n = 1..100</a>

%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)

%F G.f. = x(1+x)/(1-x-x^3+x^4) [Simplified by _N. J. A. Sloane_, Dec 06 2018]

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F (End)

%F Conjecture: a(n) = n - ceiling(n/3) = A004523(n).

%p hist2:=proc(n) local A,i,j,m,d1,d2,d3,d4;

%p A:=Array(0..n,0);

%p for i from 0 to n-1 do

%p for j from 0 to n-1 do

%p d1:=i+j;

%p d2:=n-i;

%p d3:=2*n-i-j;

%p d4:=n-j;

%p if i+j<n then

%p m:=min(d1,d2,d3,d4);

%p elif i+j=n then m:=min(i,j);

%p else

%p m:=min(d1,i,j,d3);

%p fi;

%p A[m]:=A[m]+1;

%p od: od:

%p R:=0;

%p for i from 0 to n-1 do if A[i] <> 0 then R:=i; fi; od:

%p R;

%p end;

%p RR:=[];

%p for n from 1 to 100 do RR:=[op(RR),hist2(n)]; od: RR;

%Y Cf. A322041.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Dec 06 2018

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Last modified September 20 13:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)