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
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a3 = 9
an = ((2 * n + 1)/ n + 2) * M(n-1) +((3 * n - 3)/ n + 2) * M(n - 2)
Initialise the number n.
Iterate till n.
Update the previous two numbers
Return the last number.
Following is the implementation of the above algorithm in C++
#include <bits/stdc++.h>
using namespace std;
int getNthTerm(int n) {
if(n == 0 || n == 1) {
return 1;
}
int a = 1, b = 1;
for(int i = 2; i <= n; ++i) {
int c = ((2 * i + 1) * b + (3 * i - 3) * a) / (i + 2);
a = b;
b = c;
}
return b;
}
int main() {
int n = 5;
cout << getNthTerm(n) << endl;
return 0;
}如果您运行上述代码，您将得到以下结果。
21
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