Triangular number

DIRECTORY.md

@@ -255,6 +255,7 @@
     * [Tanh](https://github.com/TheAlgorithms/Rust/blob/master/src/math/tanh.rs)
     * [Trapezoidal Integration](https://github.com/TheAlgorithms/Rust/blob/master/src/math/trapezoidal_integration.rs)
     * [Trial Division](https://github.com/TheAlgorithms/Rust/blob/master/src/math/trial_division.rs)
+    * [Triangular Number](https://github.com/TheAlgorithms/Rust/blob/master/src/math/triangular_number.rs)
     * [Trig Functions](https://github.com/TheAlgorithms/Rust/blob/master/src/math/trig_functions.rs)
     * [Vector Cross Product](https://github.com/TheAlgorithms/Rust/blob/master/src/math/vector_cross_product.rs)
     * [Zellers Congruence Algorithm](https://github.com/TheAlgorithms/Rust/blob/master/src/math/zellers_congruence_algorithm.rs)

src/math/mod.rs

@@ -78,6 +78,7 @@ mod sylvester_sequence;
 mod tanh;
 mod trapezoidal_integration;
 mod trial_division;
+mod triangular_number;
 mod trig_functions;
 mod vector_cross_product;
 mod zellers_congruence_algorithm;
@@ -170,6 +171,7 @@ pub use self::sylvester_sequence::sylvester;
 pub use self::tanh::tanh;
 pub use self::trapezoidal_integration::trapezoidal_integral;
 pub use self::trial_division::trial_division;
+pub use self::triangular_number::triangular_number;
 pub use self::trig_functions::cosine;
 pub use self::trig_functions::cosine_no_radian_arg;
 pub use self::trig_functions::cotan;

src/math/triangular_number.rs

@@ -0,0 +1,36 @@
+// Triangular Numbers: Function to the Nth Triangular Number
+// Wikipedia Reference : https://en.wikipedia.org/wiki/Triangular_number
+
+// This program provides a function to calculate the nth triangular number defined by T_n = 1 + 2 +
+// ... + n = (n^2 + 2)/2 = n(n + 1)/2 = (n + 1) choose 2.
+
+//returns the nth triangular number
+pub fn triangular_number(n: u64) -> u64 {
+    (n | 1) * ((n + 1) / 2)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    macro_rules! test_triangular_number {
+        ($($name:ident: $inputs:expr,)*) => {
+        $(
+            #[test]
+            fn $name() {
+                let (n, expected) =$inputs;
+                assert_eq!(triangular_number(n), expected);
+            }
+        )*
+        }
+    }
+
+    test_triangular_number! {
+        input_0: (0, 0),
+        input_1: (1, 1),
+        input_2: (6, 21),
+        input_3: (10, 55),
+        input_4: (21, 231),
+        input_5: (100, 5050),
+    }
+}