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A378304 Unique sequence s starting with 1,1,2,2 such that if r(r(r(s))) = s and r(s) != s and r(r(s)) != s, where r(#) denotes the runlength sequence of a sequence #.

%I A378304 #7 Dec 21 2024 02:16:46
%S A378304 1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,1,2,2,1,1,2,1,1,2,2,1,2,
%T A378304 2,1,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,2,1,2,2,1,2,1,1,2,2,1,
%U A378304 2,2,1,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1
%N A378304 Unique sequence s starting with 1,1,2,2 such that if r(r(r(s))) = s and r(s) != s and r(r(s)) != s, where r(#) denotes the runlength sequence of a sequence #.
%C A378304 This sequence is one of three limiting rows of the array A378303.  See A378282 for a guide to related arrays and sequences.
%t A378304 z = 18;
%t A378304 invRE[seq_, k_] := Flatten[Map[ConstantArray[#[[2]], #[[1]]] &,
%t A378304     Partition[Riffle[seq, {k, 2 - Mod[k + 1, 2]}, {2, -1, 2}], 2]]];
%t A378304 row1 = {1}; rows = {row1};
%t A378304 col = PadRight[{}, z, {1, 2, 2}]
%t A378304 Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]
%t A378304 rows // ColumnForm  (* A378303 *)
%t A378304 rows[[z - 2]];      (* A378304 *)
%t A378304 rows[[z - 1]];      (* A378305 *)
%t A378304 rows[[z]];          (* A378306 *)
%t A378304 Map[Length, rows] (* A378307 *)
%t A378304 (* _Peter J. C. Moses_, Nov 21 2024 *)
%Y A378304 Cf. A378282, A378303, A378305, A378306, A378307.
%K A378304 nonn
%O A378304 1,3
%A A378304 _Clark Kimberling_, Dec 20 2024