A378284 - OEIS

%I #4 Dec 21 2024 01:05:19

%S 1,2,1,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,

%T 2,1,1,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,

%U 1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,1,2

%N Unique sequence s starting with 1,2,1 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 This sequence is one of three limiting rows of the array A378282.  See A378282 for a guide to related arrays and sequences.

%t z = 18;

%t invRE[seq_, k_] := Flatten[Map[ConstantArray[#[[2]], #[[1]]] &,

%t     Partition[Riffle[seq, {k, 2 - Mod[k + 1, 2]}, {2, -1, 2}], 2]]];

%t row1 = {1}; rows = {row1};

%t col = PadRight[{}, z, {1, 1, 2}]

%t Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]

%t rows // ColumnForm

%t Flatten[rows]   (* A378282 *)

%t rows[[z - 2]];  (* A378283 *)

%t rows[[z - 1]];  (* A378284 *)

%t rows[[z]];      (* A378285 *)

%t Map[Length, rows]   (* A378286 *)

%t (* _Peter J. C. Moses_, Nov 21 2024 *)

%Y Cf. A378282, A378283, A378285, A378286, A378303.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 20 2024