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

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, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42

Offset

1,3

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..100

Formula

Conjectures from Colin Barker, Dec 06 2018: (Start)

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

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

(End)

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

Maple

hist2:=proc(n) local A, i, j, m, d1, d2, d3, d4;
A:=Array(0..n, 0);
for i from 0 to n-1 do
for j from 0 to n-1 do
d1:=i+j;
d2:=n-i;
d3:=2*n-i-j;
d4:=n-j;
if i+j<n then
   m:=min(d1, d2, d3, d4);
elif i+j=n then m:=min(i, j);
else
   m:=min(d1, i, j, d3);
fi;
   A[m]:=A[m]+1;
od: od:
R:=0;
for i from 0 to n-1 do if A[i] <> 0 then R:=i; fi; od:
R;
end;
RR:=[];
for n from 1 to 100 do RR:=[op(RR), hist2(n)]; od: RR;

Crossrefs

Cf. A322041.

Sequence in context: A156301 A195124 A032509 * A004523 A038372 A121930

Adjacent sequences: A322039 A322040 A322041 * A322043 A322044 A322045

Keyword

nonn

Author

N. J. A. Sloane, Dec 06 2018

Status

approved