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A195098 Interspersion fractally induced by (1+[3n/4]), where [ ] = floor; a rectangular array, by antidiagonals.

%I A195098 #5 Mar 30 2012 18:57:44
%S A195098 1,2,3,4,5,6,7,8,9,10,11,12,13,15,14,16,17,18,21,19,20,22,23,24,28,25,
%T A195098 26,27,29,30,31,36,32,33,34,35,37,38,39,45,40,41,42,44,43,46,47,48,55,
%U A195098 49,50,51,54,52,53,56,57,58,66,59,60,61,65,62,63,64,67,68,69
%N A195098 Interspersion fractally induced by (1+[3n/4]), where [ ] = floor; a rectangular array, by antidiagonals.
%C A195098 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194998 is a permutation of the positive integers, with inverse A195099.
%e A195098 Northwest corner:
%e A195098 1...2...4...7...11..16..22
%e A195098 3...5...8...12..17..23..30
%e A195098 6...9...13..18..24..31..39
%e A195098 10..15..21..28..36..45..55
%e A195098 14..19..25..32..40..49..59
%t A195098 r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)
%t A195098 Table[p[n], {n, 1, 90}]
%t A195098 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195098 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195098 f[20]    (* A195097 *)
%t A195098 row[n_] := Position[f[30], n];
%t A195098 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195098 v[n_, k_] := Part[row[n], k];
%t A195098 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195098 {k, 1, n}]](* A195098 *)
%t A195098 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195098 {n, 1, 80}]](* A195099 *)
%Y A195098 Cf. A194959, A037915, A195097, A195099.
%K A195098 nonn,tabl
%O A195098 1,2
%A A195098 _Clark Kimberling_, Sep 08 2011