URL: https://oeis.org/A135010/a135010.txt
(* Mathematica program to generate the "Illustration of the section model of partitions" *)
n = 6; f1 = {}; f2 = {}; x = 0; p = PartitionsP[n]; d = ConstantArray[Null, {p, n}];
For[i = n, i > 0, i--,
r = DeleteCases[Sort@PadRight[Reverse/@Cases[IntegerPartitions[i], x_ /; Last[x] != 1]], x_ /; x == 0, 2];
AppendTo[f1, {{p - PartitionsP[i] + 1, p}, {1, i}} -> Thick];
For[j = Length[r], j > 0, j--,
rj = r[[j]]; y = 1; x++;
For[k = Length[rj], k > 0, k--,
rjk = rj[[k]]; d[[x, y]] = rjk; y = y + rjk;
AppendTo[f2, {{x, x}, {y - rjk, y - 1}} -> Thin]]];
d[[p - PartitionsP[i - 1] + 1 ;; p, i]] = 1];
Grid[d, Frame -> {None, None, Join[f2, f1]}] (* Robert Price, May 12 2020 *)
