A323035 Records in A321223.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 23, 25, 26, 28, 29, 30, 32, 34, 37, 41, 42, 48, 49, 50, 51, 56, 57, 59, 61, 68, 71, 72, 75, 76, 79, 80, 81, 82, 84, 86, 88, 89, 92, 93, 100, 103, 108, 118, 119, 120, 122, 125, 129, 130, 135, 141, 143

Offset: 1

Author

Michael De Vlieger, Jan 04 2019

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..381
• William J. Keith, Recursively Self-Conjugate Partitions, Integers 11A, (2011) Article 12.

Crossrefs

Cf. A190899, A190900, A321223, A322156, A322457.

Programs

Mathematica

f[w_] := Block[{k}, k = Total@ w; Total@ Map[Apply[Function[{s, t}, s Array[Boole[t <= # <= s + t - 1] &, k] ], #] &, Apply[Join, Prepend[Table[Function[{v, c}, Map[{w[[k]], # + 1} &, Map[Total[v #] &, Tuples[{0, 1}, {Length@ v}]]]] @@ {Most@ #, ConstantArray[1, Length@ # - 1]} &@ Take[w, k], {k, 2, Length@ w}], {{w[[1]], 1}}]]] ]; g[n_] := Block[{w = {n}, c}, c[x_] := Apply[Times, Most@ x - Reverse@ Accumulate@ Reverse@ Rest@ x]; Reap[Do[Which[And[Length@ w == 2, SameQ @@ w], Sow[w]; Break[], Length@ w == 1, Sow[w]; AppendTo[w, 1], c[w] > 0, Sow[w]; AppendTo[w, 1], True, Sow[w]; w = MapAt[1 + # &, Drop[w, -1], -1] ], {i, Infinity}] ][[-1, 1]] ]; Block[{n = 40, a}, a = Merge[Map[<| #1 -> #2 |> & @@ # &, #], Identity] &@ TakeWhile[Sort@ Map[{Total@ #2, #1, #2} & @@ {#, f[#]} &, Apply[Join, Array[g, n]] ], First@ # <= n^2 &][[All, 1 ;; 2]]; Union@ FoldList[Max, Array[Length[Lookup[a, #] /. k_ /; MissingQ@ k -> {}] &, Length@ a]]]