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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 Cf. A194029, A194049. Sequence in context: A085436 A277710 A286148 * A158868 A104634 A194008 Adjacent sequences:  A194045 A194046 A194047 * A194049 A194050 A194051 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 13 2011 STATUS approved

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Last modified January 24 23:49 EST 2021. Contains 340414 sequences. (Running on oeis4.)