

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
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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, 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



