please answer question 3 b) 2. Prove that 1m+2ml (n+1 and use this to find a for
ID: 3607415 • Letter: P
Question
please answer question 3 b)
2. Prove that 1m+2ml (n+1 and use this to find a formula for 12+22+3++ 3. Find generating series for the number of (a) binary strings of length n that do not contain the substring 1100 (b) binary strings of length n that to not contain the substring 1011 (c) words of length n on the alphabet ta, b, el such that b is never adjacent to c (d) compositions of n in which no two consecutive parts are equal to 1 4. (Bonus) Let tn be the number of tilings of a 2 x n rectangle using 2 x 1 and 1 x 1 tiles a closed form for the generating series T(z)- nso tna" and use it to give a recurre tn), along with initial conditions.Explanation / Answer
#include<iostream.h>
#include<conio.h>
#include<string.h>
#include<stdlib.h>
void main()
{
char s[100]; char s1[4]="1011"; int i=0,j=0,k=0,x=0,p=0,c=0,n=0,num=0;
clrscr();
randomize();
cout<<" enter no of strings to generate";
cin>>num;
cout<<" enter string length";
cin>>n;
for(k=1;k<=num;k++)
{
//following loop will generate binary strings
for(i=0;i<n;i++)
{
x=random(2);
if(x==0)s[i]='0';
else s[i]='1';
}//for
s[i]='';
for(i=0;i<strlen(s);i++)
{
p=0,c=0;
//foll loop is checking if any four consecutive chars are 1011
for(int m=1,j=i;m<=4;m++,j++)
{
if(s[j]==s1[p])
{
c++;p++;
}
}//if
// when 4 consecutive chars are 1011 the this string is not printed and next string is examined
if(c==4)
{ k--;
break;
}
}
if(c!=4)
cout<<" "<<s;
}
getch();
}
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