cp's OEIS Frontend

Maple

ChessKingPaths := proc(N, aUsed:=[1])
  local nLast, nPrev,  nNext,  i, j, i1, j1, i2, j2:
  global aPath, nPaths;
if N=1 then
  aPath:=[[1]]; nPaths:=1; return nPaths;
end if:
  if aUsed=[1] then
    aPath:=[]; nPaths:=0;
  end if;
  nLast:=N^(2);   #`opposite corner`
  nPrev := aUsed[-1] ; #actual position
  #Check all possible next cells
  i1:=`if`(floor((nPrev-1)/N)=0,0,-N); i2:=`if`(floor((nPrev-1)/N)=N-1,0,N);
  j1:=`if`((nPrev-1)mod N=0,0,-1); j2:=`if`((nPrev-1) mod N=N-1,0,1);
  for i from i1 to i2 by N do
    for j from j1 to j2 by 1 do
      if i=0 and j=0 then next fi; #`no move`
      nNext:=nPrev+i+j;
      #`out of bounds or already visited`
      if nNext<1 or nNext>nLast or (nNext in aUsed) then next: fi;
      #`nLast must be the last one`
      if (nNext=nLast and nops(aUsed)<>nLast-1) then next fi:
      if nNext=nLast  and nops(aUsed)=nLast-1 then  #`path completed`
        #comment if list is not required. It will consume all memory for N>=5
        aPath:=[op(aPath), [op(aUsed),nNext]];
        nPaths:=nPaths+1;
        break:
      else
        ChessKingPaths(N,[op(aUsed),nNext]) #move and continue
      end if;
    end do:
  end do:
  return nPaths;
end proc:
#For a(n) call this function with parameter n.
#Examples: ChessKingPaths(2), ChessKingPaths(3),...
#The list of paths is stored in variable aPath.