The Motzkin number series starts with 1, 1, 4, 9, etc.., We can get the generalised nth term with the sequence. The Motzkin number sequence is as follows.
a0 = 1
a1 = 1
a2 = 4
a3 = 9
an = ((2 * n + 1)/ n + 2) * M(n-1) +((3 * n – 3)/ n + 2) * M(n – 2)
Algorithm
-
Initialise the number n.
-
Iterate till n.
-
Update the previous two numbers
-
-
Return the last number.
Example
Implementation
Following is the implementation of the above algorithm in C++
#include
using namespace std;
int getNthTerm(int n) {
if(n == 0 || n == 1) {
return 1;
}
int a = 1, b = 1;
for(int i = 2; i
