ocaml: phase 5.1 partition_count.ml baseline (p(15) = 176)

Counts integer partitions via classic DP:

  let partition_count n =
    let dp = Array.make (n + 1) 0 in
    dp.(0) <- 1;
    for k = 1 to n do
      for i = k to n do
        dp.(i) <- dp.(i) + dp.(i - k)
      done
    done;
    dp.(n)

  partition_count 15 = 176

Tests Array.make, .(i)<-/.(i) array access, nested for-loops, refs.

135 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — partition_count.ml baseline (number of
+  integer partitions of 15 = 176). Classic DP: dp[0] = 1; for each
+  k from 1..n, for each i from k..n, dp[i] += dp[i - k]. O(n²) time,
+  O(n) space. p(15) = 176 partitions of 15. Tests Array.make, array
+  set/get with `.(i)<-` / `.(i)`, nested for-loops, ref deref.
+  135 baseline programs total.
 - 2026-05-10 Phase 5.1 — pythagorean.ml baseline (count primitive
   Pythagorean triples with hypotenuse ≤ 100 = 16). Uses Euclid's
   formula: for coprime m > k of opposite parity, the triple