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Finding recurrence relation from combinatorics formulas

For example let f(n)=nC0+(n-1)C1+(n-2)C2+(n-3)C3 +...........+(n-k)Ck; where k<=n/2;

1<=n<=10^7

How will we solve it ?

I know recusrsive function f(n)=f(n-1)+f(n-2)+1 will solve it .

But i want to general methods to solve this type of questions of converting formulae to recursion.

Here is another problem Magic Gems. its function is f(n,m)=nC0+(n-(m-1))C1+(n-2(m-1))C2+(n-3(m-1))C3+............

Please suggest way to solve above problem

asked 19 Feb, 00:21

saurabh_mittal's gravatar image

3★saurabh_mittal
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accept rate: 0%

edited 19 Feb, 00:28

(19 Feb, 02:00) meooow ♦6★
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question asked: 19 Feb, 00:21

question was seen: 113 times

last updated: 19 Feb, 02:00