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A356380 Main diagonal of the LIRO variant of the array A035486; this is one of eight such sequences discussed in A007063.

%I A356380 #6 Nov 09 2022 19:16:54
%S A356380 1,3,5,6,4,11,13,2,7,14,24,9,10,31,35,33,27,23,38,42,46,54,37,44,52,
%T A356380 34,17,21,26,77,79,45,28,40,12,70,36,72,69,66,90,75,47,67,95,76,126,
%U A356380 43,108,87,74,133,88,60,116,99,102,86,151,111,156,169,173,171
%N A356380 Main diagonal of the LIRO variant of the array A035486; this is one of eight such sequences discussed in A007063.
%C A356380 Conjecture:  every positive integer occurs exactly once.
%t A356380 lori = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],
%t A356380       Range[(Length[#] + 3)/2, Length[#]]]]],
%t A356380       Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]];
%t A356380 s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[
%t A356380       ToExpression[#]]} &, {"lori"}];
%t A356380 Last[First[s]]   (* A356379 *)
%t A356380 (* _Peter J. C. Moses_, Jul 26 2022 *)
%t A356380 (* The next program generates the LIRO array. *)
%t A356380 len = 8; liro = Join[{{1}}, NestList[Join[#[[Riffle[Range[(Length[#] - 1)/2, 1, -1],
%t A356380      Range[Length[#], (Length[#] + 3)/2, -1]]]],
%t A356380      Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, len]];
%t A356380 Grid[Map[Flatten, Transpose[{#, Range[3 Range[Length[#]] - 1,
%t A356380        4 (Length[#] - 2) - 1 + Range[Length[#]]]}]] &[liro]]
%t A356380 (* _Peter J. C. Moses_, Aug 02 2022 *)
%Y A356380 Cf. A007063, A035486.
%K A356380 nonn
%O A356380 1,2
%A A356380 _Clark Kimberling_, Oct 24 2022