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%I #5 Mar 30 2012 18:57:40
%S 1,4,2,9,5,3,15,10,6,7,23,16,11,12,8,33,24,17,18,13,14,45,34,25,26,19,
%T 20,21,58,46,35,36,27,28,29,22,73,59,47,48,37,38,39,30,31,90,74,60,61,
%U 49,50,51,40,41,32,109,91,75,76,62,63,64,52,53,42,43,129,110
%N Natural interspersion of A194106; a rectangular array, by antidiagonals.
%C 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, A194108 is a permutation of the positive integers; its inverse is A194109.
%e Northwest corner:
%e 1...4...9...15...23
%e 2...5...10..16...24
%e 3...6...11..17...25
%e 7...12..18..26...36
%e 8...13..19..27...37
%t z = 40; g = Sqrt[3];
%t c[k_] := Sum[Floor[j*g], {j, 1, k}];
%t c = Table[c[k], {k, 1, z}] (* A194106 *)
%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t f = Table[f[n], {n, 1, 800}] (* A194107 *)
%t r[n_] := Flatten[Position[f, n]]
%t t[n_, k_] := r[n][[k]]
%t TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]] (* A194108 *)
%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194109 *)
%Y Cf. A194029, A194106, A194107, A194109.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 15 2011
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