cp's OEIS Frontend

A195077 Interspersion fractally induced by A009620, a rectangular array, by antidiagonals.

%I A195077 #10 May 11 2013 11:29:45
%S A195077 1,3,2,6,4,5,10,7,9,8,15,11,14,13,12,21,16,20,19,17,18,28,22,27,26,23,
%T A195077 25,24,36,29,35,34,30,33,32,31,45,37,44,43,38,42,41,39,40,55,46,54,53,
%U A195077 47,52,51,48,50,49,66,56,65,64,57,63,62,58,61,60,59,78,67,77
%N A195077 Interspersion fractally induced by A009620, a rectangular array, by antidiagonals.
%C A195077 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194977 is a permutation of the positive integers, with inverse A195078.  A195077 is not A194915.
%t A195077 r = 3; p[n_] := 1 + Floor[n/r]
%t A195077 Table[p[n], {n, 1, 90}]  (* A009620 *)
%t A195077 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195077 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195077 f[20] (* A195076 *)
%t A195077 row[n_] := Position[f[30], n];
%t A195077 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195077 v[n_, k_] := Part[row[n], k];
%t A195077 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195077 {k, 1, n}]]  (* A195077 *)
%t A195077 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195077 {n, 1, 80}]]  (* A195078 *)
%Y A195077 Cf. A194959, A009620, A195076, A195078.
%K A195077 nonn,tabl
%O A195077 1,2
%A A195077 _Clark Kimberling_, Sep 08 2011