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A195080 Interspersion fractally induced by A008621, a rectangular array, by antidiagonals. 3
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, 24, 23, 36, 35, 29, 34, 33, 32, 30, 31, 45, 44, 37, 43, 42, 41, 38, 40, 39, 55, 54, 46, 53, 52, 51, 47, 50, 49, 48, 66, 65, 56, 64, 63, 62, 57, 61, 60, 59, 58, 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, A194980 is a permutation of the positive integers, with inverse A195081.

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

Northwest corner:

1...3...6...10..15..21..38

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 = 4; p[n_] := 1 + Floor[n/r]

Table[p[n], {n, 1, 90}]  (* A008621 *)

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] (* A195079 *)

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}]] (* A195080 *)

q[n_] := Position[w, n]; Flatten[Table[q[n],

{n, 1, 80}]] (* A195081 *)

CROSSREFS

Cf. A008621, A195079, A195081.

Sequence in context: A195081 A120913 A194922 * A194858 A194857 A194879

Adjacent sequences:  A195077 A195078 A195079 * A195081 A195082 A195083

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.)