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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)