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A194048 Natural interspersion of A000330, a rectangular array, by antidiagonals. 2
1, 5, 2, 14, 6, 3, 30, 15, 7, 4, 55, 31, 16, 8, 9, 91, 56, 32, 17, 18, 10, 140, 92, 57, 33, 34, 19, 11, 204, 141, 93, 58, 59, 35, 20, 12, 285, 205, 142, 94, 95, 60, 36, 21, 13, 385, 286, 206, 143, 144, 96, 61, 37, 22, 23 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194048 is a permutation of the positive integers; its inverse is A194049.
LINKS
EXAMPLE
Northwest corner:
1...5...14...30...55
2...6...15...31...56
3...7...16...32...57
4...8...17...33...58
9...18..34...59...95
MATHEMATICA
Remove["Global`*"];
z = 30;
c[k_] := k (k + 1) (2 k + 1)/6;
c = Table[c[k], {k, 1, z}] (* A000330 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 500}] (* fractal sequence [A064866] *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 10}, {k, 1, n}]] (* A194048 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194049 *)
CROSSREFS
Sequence in context: A277710 A286148 A369369 * A158868 A104634 A194008
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 13 2011
STATUS
approved

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)