%I #6 Nov 09 2022 19:16:18
%S 1,3,5,6,4,11,12,9,13,15,23,7,27,16,24,25,34,36,19,14,50,41,10,40,60,
%T 32,43,35,26,20,38,63,79,81,57,44,74,80,65,72,107,28,53,93,76,66,114,
%U 56,129,55,119,47,103,125,85,39,45,141,106,77,98,137,109,33
%N Main diagonal of the LORO variant of the array A035486; this is one of eight such sequences discussed in A007063.
%C Conjecture: every positive integer except 2 occurs exactly once.
%t loro = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],
%t Range[Length[#], (Length[#] + 3)/2, -1]]]],
%t Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]];
%t s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[
%t ToExpression[#]]} &, {"loro"}]; u = Last[First[s]]
%t (* _Peter J. C. Moses_, Jul 26 2022 *)
%t (* The next program generates the LORO array. *)
%t len = 8; loro = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],
%t Range[Length[#], (Length[#] + 3)/2, -1]]]],
%t Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, len]];
%t Grid[Map[Flatten, Transpose[{#, Range[3 Range[Length[#]] - 1,
%t 4 (Length[#] - 2) - 1 + Range[Length[#]]]}]] &[loro]]
%t (* _Peter J. C. Moses_, Aug 02 2022 *)
%Y Cf. A007063, A035486.
%K nonn
%O 1,2
%A _Clark Kimberling_, Oct 21 2022
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