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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
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.
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