

A194922


Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.


4



1, 3, 2, 6, 5, 4, 10, 9, 7, 8, 15, 14, 11, 13, 12, 21, 20, 16, 19, 18, 17, 28, 27, 22, 26, 25, 23, 24, 36, 35, 29, 34, 33, 30, 32, 31, 45, 44, 37, 43, 42, 38, 41, 40, 39, 55, 54, 46, 53, 52, 47, 51, 50, 49, 48, 66, 65, 56, 64, 63, 57, 62, 61, 60, 58, 59, 78, 77, 67
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OFFSET

1,2


COMMENTS

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194922 is a permutation of the positive integers, with inverse A195071.


LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened


EXAMPLE

Northwest corner:
1, 3, 6, 10, 15, 21
2, 5, 9, 14, 20, 27, 35
4, 7, 11, 16, 22, 29, 37
8, 13, 19, 26, 34, 43, 53
12, 18, 25, 33, 42, 52, 63


MATHEMATICA

r = Sqrt[2]; p[n_] := n  Floor[n/r]
Table[p[n], {n, 1, 90}] (* A194920 *)
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] (* A194921 *)
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}]] (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195071 *)


CROSSREFS

Cf. A194920, A194921, A195071.
Sequence in context: A195071 A195081 A120913 * A195080 A194858 A194857
Adjacent sequences: A194919 A194920 A194921 * A194923 A194924 A194925


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Sep 08 2011


STATUS

approved



