OFFSET
1,3
COMMENTS
See A194832 for a general discussion.
EXAMPLE
First nine rows:
1
1 2
3 1 2
3 1 4 2
5 3 1 4 2
5 3 1 6 4 2
7 5 3 1 6 4 2
7 5 3 1 8 6 4 2
9 7 5 3 1 8 6 4 2
MATHEMATICA
r = Sqrt[12];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194899 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 15},
{k, 1, n}]] (* A194900 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 90}]] (* A194901 *)
PROG
(PARI) row(n) = Vec(vecsort(vector(n, k, frac(k*sqrt(12))), , 1));
tabl(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Feb 06 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 05 2011
STATUS
approved