What is
`2^(10) - ( (10) ,(4) )`
?These binary strings biject to non-negative integer solutions to
`a+b+c+d+e = 148`
`1/(1-(x^2+x^7+x^9))?`
This recurrence relation has generating function
`f(x) = ( a_0 + (a_1 - 3a_0) x ) / ( 1 - 3x + 2x^2 )`
`a_(n+2) = 3a_(n+1) - 2a_(n)`
?
`20 ->18.`
What is
`sum_{k=0}^18 (-1)^k ((18),(k)) (18-k)^(20)?`
(There's also no identity.)
`O( n^(m-1) lambda^n)`
where
`lambda`
is the largest eigenvalue and has multiplicity m.
`B_{26} = \sum_{k=1}^{26} {(26),(k):}}?`
`a_n = (1+n)5^n`
?It satisfies a_0 = 1 and a_1 = 10 and the recurrence relation
`a_n = 10 a_{n-1}-25a_{n-2}`
"As a base case a single vertex is 2-colorable. Suppose that every tree with k vertices is 2-colorable. Let T be a tree with k+1 vertices. Then T must have a degree 1 vertex v attached to some vertex u. By the inductive hypothesis deleting edge {u,v} and v from T gives a 2-colorable graph. Then coloring v the color u is not colored gives a 2-coloring of T."
?
The total number of length 10 strings on {a,b,c,d} is more than this number of strings on {a,b,c,d} considered up to cyclic permutation. ( Cyclic permutation: abc ~ bca ~ cba )
What is
`( 4^10 + 4 * 4^5 + 4^2 + 4*4 ) / 10?`