OFFSET
1,2
COMMENTS
See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
LINKS
G. C. Greubel, Antidiagonals n = 0..50, flattened
EXAMPLE
Northwest corner:
1...2...4...7..11..16..22
3...5...9..14..20..27..35
6..10..15..21..28..36..45
8..12..17..23..30..38..47
18..13..25..33..42..52..63
Antidiagonals of the array:
1;
2, 3;
4, 5, 6;
7, 9, 10, 8;
11, 14, 15, 12, 13;
16, 20, 21, 17, 18, 19;
22, 27, 28, 23, 25, 26, 24;
29, 35, 36, 30, 33, 34, 31, 32;
37, 44, 45, 38, 42, 43, 39, 40, 41;
MATHEMATICA
p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]
Table[p[n], {n, 1, 90}] (* A194960 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A194961 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A194962 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]] (* A194963 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 07 2011
STATUS
approved