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A194969
Interspersion fractally induced by A194968, a rectangular array, by antidiagonals.
4
1, 2, 3, 4, 6, 5, 7, 10, 8, 9, 11, 15, 12, 13, 14, 16, 21, 17, 18, 20, 19, 22, 28, 23, 24, 27, 25, 26, 29, 36, 30, 31, 35, 32, 34, 33, 37, 45, 38, 39, 44, 40, 43, 41, 42, 46, 55, 47, 48, 54, 49, 53, 50, 51, 52, 56, 66, 57, 58, 65, 59, 64, 60, 61, 63, 62, 67, 78, 68
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, A194969 is a permutation of the positive integers, with inverse A194970.
EXAMPLE
Northwest corner:
1...2...4...7...11..16
3...6...10..15..21..28
5...8...12..17..23..30
9...13..18..24..31..39
14..20..27..35..44..54
MATHEMATICA
r = GoldenRatio; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}] (* A019446 *)
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] (* A194968 *)
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}]] (* A194969 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194970 *)
CROSSREFS
Cf. A194958, A019446, A194968, A194970 (inverse).
Sequence in context: A064578 A371247 A361251 * A194981 A057027 A371246
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 07 2011
STATUS
approved