Discrete Mathem...

What is the generating function of the sequence {1,1,3,1,1,1,1……………}?

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

If the recurrence relation capturing the optimal execution time of the towers of Hanoi problem with n discs is T(n) = 2T(n - 1) + 1 then what is the value of T(7)?

The coefficient of x²⁰ in the expansion of (x³ + x⁴ + x⁵ + …………)⁵ is _____.

What could be the solution for the equation T (n) = 10 T(n-1) – 25 T(n-2)

Consider the recurrence relation a₁ = 8, a_n = 6n² + 2n + a_n-1. Let a₉₉ = K × 10⁴. The value of K is.

Which of the following is/are closed form expression for the generating function of the sequence {an} where \({a_n} = 5n + 2\) for all n = 0, 1, 2, 3, …? 

If \({a_n} = {\alpha _1}{\left( {{r_1}} \right)^n} + {a_2}{\left( {{r_2}} \right)^n}\) is the solution of the recurrence relation \({a_n} = 5{a_n}_{ - 1} - \;6{a_n}_{ - 2}\) with initial condition \({a_0}\) = 1 and  \({r_1}\), \({r_2}\) are characteristic root then what is the sum of \(({\alpha _1} + {\alpha _2} + {r_1} + {r_{2\;}})\)?