Alternative AWK solution for week 104, part 1

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diff --git a/challenge-104/abigail/awk/ch-1a.awk b/challenge-104/abigail/awk/ch-1a.awk
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+#!/usr/bin/awk
+
+#
+# See ../README.md
+#
+
+#
+# Run as: awk -f ch-1a.awk < input-file
+#
+
+#
+# Instead of doing the simple thing (print a fixed string), which
+# we've done in ch-1.awk, here we will actually calculate the numbers.
+#
+
+#
+# Initialize the cache
+#
+BEGIN {
+    cache [0] = 0
+    cache [1] = 1
+}
+
+#
+# Calculate the nth FUSC number, using a cache.
+#
+function fusc (n) {
+    if (!(n in cache)) {
+        cache [n] = n % 2 ? fusc((n - 1) / 2) + fusc((n + 1) / 2) \
+                          : fusc( n      / 2)
+    }
+    return (cache [n])
+}
+
+#
+# Print the first 50 numbers.
+#
+BEGIN {
+    for (i = 0; i < 50; i ++) {
+        printf "%s%d", (i == 0 ? "" : " "), fusc(i)
+    }
+    print
+}
+