modified: Math/faulhaber_s_formula_explicit.sf

Author: trizen

Math/faulhaber_s_formula_explicit.sf

@@ -1,24 +1,8 @@
 #!/usr/bin/ruby
 
-#
-## http://rosettacode.org/wiki/Faulhaber%27s_formula
-#
-
-func bernoulli({.is_one}) { 1/2 }
-func bernoulli({.is_odd}) { 0/1 }
-
-func bernoulli(n) {
-
-    var a = []
-    for m in ^(n+1) {
-        a[m] = 1/(m + 1)
-        for j in (m^..0 + 1) {
-            a[j-1] = j*(a[j-1] - a[j])
-        }
-    }
-
-    return a[0]
-}
+# See also:
+#   https://en.wikipedia.org/wiki/Faulhaber%27s_formula
+#   https://rosettacode.org/wiki/Faulhaber%27s_formula
 
 func faulhaber_s_formula(p) {
 
@@ -37,6 +21,18 @@ func faulhaber_s_formula(p) {
     "1/#{p + 1} * (#{formula})"
 }
 
-for p in ^10 {
-    printf("%2d: %s\n", p, faulhaber_s_formula(p))
+10.times {|p|
+    printf("F(%s) = %s\n", p, faulhaber_s_formula(p))
 }
+
+__END__
+F(0) = 1/1 * (n)
+F(1) = 1/2 * (n^2 + n)
+F(2) = 1/3 * (n^3 + 3/2*n^2 + 1/2*n)
+F(3) = 1/4 * (n^4 + 2*n^3 + n^2)
+F(4) = 1/5 * (n^5 + 5/2*n^4 + 5/3*n^3 + -1/6*n)
+F(5) = 1/6 * (n^6 + 3*n^5 + 5/2*n^4 + -1/2*n^2)
+F(6) = 1/7 * (n^7 + 7/2*n^6 + 7/2*n^5 + -7/6*n^3 + 1/6*n)
+F(7) = 1/8 * (n^8 + 4*n^7 + 14/3*n^6 + -7/3*n^4 + 2/3*n^2)
+F(8) = 1/9 * (n^9 + 9/2*n^8 + 6*n^7 + -21/5*n^5 + 2*n^3 + -3/10*n)
+F(9) = 1/10 * (n^10 + 5*n^9 + 15/2*n^8 + -7*n^6 + 5*n^4 + -3/2*n^2)