Faulhaber's triangle: Difference between revisions

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 }
-#
-## First 10 rows of Faulhaber's triangle:
-#
 { |p|
     say faulhaber_triangle(p).map{ '%6s' % .as_rat }.join
 } << 1..10
-#
-## Extra credit:
-#
 const p = 17
 const n = 1000
@@ Line 1,823: / Line 1,817: @@
 56056972216555580111030077961944183400198333273050000
+</pre>
+Alternative solution:
+<lang ruby>func find_poly_degree(a) {
+    var c = 0
+    loop {
+        ++c
+        a = a.map_cons(2, {|n,k| n-k })
+        return 0 if a.is_empty
+        return c if a.all { .is_zero }
+    }
+}
+func faulhaber_triangle(n) {
+    var a = (0..(n+2) -> accumulate { _**n })
+    var c = find_poly_degree(a)
+    var A = c.of {|n|
+        c.of {|k| n**k }
+    }
+    A.msolve(a).slice(1)
+}
+.times { say faulhaber_triangle(_) }</lang>
+{{out}}
+<pre>
+[1]
+[1/2, 1/2]
+[1/6, 1/2, 1/3]
+[0, 1/4, 1/2, 1/4]
+[-1/30, 0, 1/3, 1/2, 1/5]
+[0, -1/12, 0, 5/12, 1/2, 1/6]
+[1/42, 0, -1/6, 0, 1/2, 1/2, 1/7]
+[0, 1/12, 0, -7/24, 0, 7/12, 1/2, 1/8]
+[-1/30, 0, 2/9, 0, -7/15, 0, 2/3, 1/2, 1/9]
+[0, -3/20, 0, 1/2, 0, -7/10, 0, 3/4, 1/2, 1/10]
 </pre>