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Combinatorics | Number Theory
Solve the recurrence relation a_n=-3a_(n-1)-3a_(n-2)-a_(n-3) with a_0=5,a_1=-9,and a_2=15.
Combinatorics | Number Theory
Solve the recurrence relationa_n=6a_(n-1)-12a_(n-2)+8a_(n-3) with a_0=-5,a_1=4,and a_2=88.
Combinatorics | Number Theory
Find an explicit formula for the Fibonacci numbers.
Combinatorics | Number Theory
How many bit sequences of length seven contain an even number of 0s?
Combinatorics | Number Theory
Find a recurrence relation for the number of bit sequences of length n with an even number of 0s.
Combinatorics | Number Theory
Solve a_n=6a_(n-1)-9a_(n-2)+F(n) when
(i)F(n)=3n
(ii) F(n)=n3^n
(iii) F(n)=n^2 2^n
(iv)F(n)=〖(n〗^2+1).3^n
(i)F(n)=3n
(ii) F(n)=n3^n
(iii) F(n)=n^2 2^n
(iv)F(n)=〖(n〗^2+1).3^n
Combinatorics | Number Theory
Show that the sequence 〖{a〗_n} is a solution of the recurrence relation a_n=a_(n-1)+〖2a〗_(n-2)+2n-9 if
(i)〖 a〗_n=-n+2
(ii) a_n=〖5(-1)〗^n-n+2
(iii) 〖3(-1)〗^n+2^n-n+2
(iv)〖7.2〗^n-n+2
(i)〖 a〗_n=-n+2
(ii) a_n=〖5(-1)〗^n-n+2
(iii) 〖3(-1)〗^n+2^n-n+2
(iv)〖7.2〗^n-n+2
Combinatorics | Number Theory
Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s. Find also the initial conditions?
Combinatorics | Number Theory
Is the sequence 〖{a〗_n} a solution of the recurrence relation a_n=8a_(n-1)-16a_(n-2)if a_n=n^4 a_n=0.
Combinatorics | Number Theory
In a company, ID cards have 5 digit numbers.
a) How many ID cards can be formed if repetion of the digit is allowed?
b) How many ID cards can be formed if repetion of the digit is not allowed?
a) How many ID cards can be formed if repetion of the digit is allowed?
b) How many ID cards can be formed if repetion of the digit is not allowed?
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