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Task/Paraffins/Pascal/paraffins.pascal

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+Program Paraffins;
+
+uses
+  gmp;
+
+const
+  max_n = 500;
+  branch = 4;
+
+var
+  rooted, unrooted: array [0 .. max_n-1] of mpz_t;
+  c: array [0 .. branch-1] of mpz_t;
+  cnt, tmp: mpz_t;
+  n: integer;
+  fmt: pchar;
+  sum: integer;
+
+procedure tree(br, n, l: integer; sum: integer; cnt: mpz_t);
+  var
+    b, m: integer;
+  begin
+    for b := br + 1 to branch do
+    begin
+      sum := sum + n;
+      if sum >= max_n then
+	exit;
+
+      (* prevent unneeded long math *)
+      if (l * 2 >= sum) and (b >= branch) then
+	exit;
+
+      if b = (br + 1) then
+	mpz_mul(c[br], rooted[n], cnt)
+      else
+      begin
+	mpz_add_ui(tmp, rooted[n], b - br - 1);
+	mpz_mul(c[br], c[br], tmp);
+	mpz_divexact_ui(c[br], c[br], b - br);
+      end;
+
+      if l * 2 < sum then
+	mpz_add(unrooted[sum], unrooted[sum], c[br]);
+
+      if b < branch then
+      begin
+	mpz_add(rooted[sum], rooted[sum], c[br]);
+	for m := n-1 downto 1 do
+	  tree(b, m, l, sum, c[br]);
+      end;
+    end;
+  end;
+
+procedure bicenter(s: integer);
+begin
+  if odd(s) then
+    exit;
+  mpz_add_ui(tmp, rooted[s div 2], 1);
+  mpz_mul(tmp, rooted[s div 2], tmp);
+  mpz_tdiv_q_2exp(tmp, tmp, 1);
+
+  mpz_add(unrooted[s], unrooted[s], tmp);
+end;
+
+begin
+  for n := 0 to 1 do
+  begin
+    mpz_init_set_ui(rooted[n], 1);
+    mpz_init_set_ui(unrooted[n], 1);
+  end;
+  for n := 2 to max_n-1 do
+  begin
+    mpz_init_set_ui(rooted[n], 0);
+    mpz_init_set_ui(unrooted[n], 0);
+  end;
+  for n := 0 to BRANCH-1 do
+    mpz_init(c[n]);
+
+  mpz_init(tmp);
+
+  mpz_init_set_ui(cnt, 1);
+  sum := 1;
+  for n := 1 to MAX_N do
+  begin
+    tree(0, n, n, sum, cnt);
+    bicenter(n);
+    mp_printf('%d: %Zd'+chr(13)+chr(10), n, @unrooted[n]);
+  end;
+end.