Fibonacci.

expreduce/builtin_numbertheory.go

@@ -151,5 +151,6 @@ func GetNumberTheoryDefinitions() (defs []Definition) {
 	defs = append(defs, Definition{Name: "IntegerPart"})
 	defs = append(defs, Definition{Name: "PowerMod"})
 	defs = append(defs, Definition{Name: "EulerPhi"})
+	defs = append(defs, Definition{Name: "Fibonacci"})
 	return
 }

expreduce/evalstate.go

@@ -348,6 +348,13 @@ func ruleSpecificity(lhs Ex, rhs Ex, name string) int {
 	if name == "Rubi`Int" {
 		return 100
 	}
+	// Special case for single integer arguments.
+	expr, isExpr := lhs.(*Expression).Parts[1].(*Expression)
+	if isExpr && len(expr.Parts) == 2 {
+		if _, isInt := expr.Parts[1].(*Integer); isInt {
+			return 110
+		}
+	}
 	// I define complexity as the length of the Lhs.String()
 	// because it is simple, and it works for most of the common cases. We wish
 	// to attempt f[x_Integer] before we attempt f[x_]. If LHSs map to the same

expreduce/resources/numbertheory.m

@@ -252,3 +252,14 @@
         ESameTest[1,EulerPhi[-1]],
     ]
 };
+
+Fibonacci::usage = "`Fibonacci[n]` computes the Fibonacci number for `n`";
+Fibonacci[0] = 0; Fibonacci[1] = 1;
+(*TODO: implement as RootReduce@(((1 + Sqrt[5])/2)^n - ((1 - Sqrt[5])/2)^n)/Sqrt[5]*)
+Fibonacci[n_] := Fibonacci[n] = Fibonacci[n - 1] + Fibonacci[n - 2];
+Attributes[Fibonacci] = {Listable, NumericFunction, Protected, ReadProtected};
+Tests`Fibonacci = {
+    ESimpleExamples[
+        ESameTest[6765, Fibonacci[20]]
+    ]
+};