A356380 - OEIS

%I #6 Nov 09 2022 19:16:54

%S 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 34,17,21,26,77,79,45,28,40,12,70,36,72,69,66,90,75,47,67,95,76,126,

%U 43,108,87,74,133,88,60,116,99,102,86,151,111,156,169,173,171

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

%C Conjecture:  every positive integer occurs exactly once.

%t lori = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],

%t       Range[(Length[#] + 3)/2, Length[#]]]]],

%t       Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]];

%t s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[

%t       ToExpression[#]]} &, {"lori"}];

%t Last[First[s]]   (* A356379 *)

%t (* _Peter J. C. Moses_, Jul 26 2022 *)

%t (* The next program generates the LIRO array. *)

%t len = 8; liro = Join[{{1}}, NestList[Join[#[[Riffle[Range[(Length[#] - 1)/2, 1, -1],

%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[#]]]}]] &[liro]]

%t (* _Peter J. C. Moses_, Aug 02 2022 *)

%Y Cf. A007063, A035486.

%K nonn

%O 1,2

%A _Clark Kimberling_, Oct 24 2022