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

1,2

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.

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]]]

Crossrefs

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

Sequence in context: A347527 A022766 A249611 * A372657 A097745 A032965

Adjacent sequences: A323032 A323033 A323034 * A323036 A323037 A323038

Keyword

nonn

Author

Michael De Vlieger, Jan 04 2019

Status

approved