The meaning of problems
\ (n \) personal, everyone can stand the red team, blue team can stand, also when the observer.
Red team wins if and only if the number is greater than the number of stations Red Team Blue Team station.
He asked several red team winning program, a small number of quality \ (p \) modulo.
\ (n-\ Leq} ^ {10} {18 is, P \ Leq ^ {10}. 6} {\) .
answer
List equation:
\ [\ sum_ {I} = 0 n-^ \ n-Binom {} {I} \ sum_ {J} = 0 {^ \ lfloor \ {n-FRAC - I -. 1} {2} \} rfloor \ binom {n - i} {
j} \] found that this latter corresponds to the thing
\ [\ sum_ {i = 0 } ^ n \ binom {n} {i} 2 ^ {n - i - 1} - \ sum_ { i = 0} ^ n \ binom
{n} {i} {n \ binom - i} {i} \] about to lose the red team program minus the number of non-red team level results obtained program number.
Find the above thing is equal to
\ [\ frac {1} { 2} \ left (3 ^ n - \ sum_ {i = 0} ^ n \ binom {n} {i} \ binom {n - i} {i} \ right) \]
this is how things count?