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Some properties of leetcode139 Yang Hui triangle
2022-07-07 10:22:00 【qq_ forty-two million one hundred and twenty thousand eight hun】
Yang Hui triangle has special properties
- Each line of numbers is symmetrical from 1 Start getting bigger and smaller , And finally back to 1.
- The first n That's ok ( from 0 open beginning Ed Number ) Count word Yes n + 1 term , front n That's ok common Yes n ( n + 1 ) 2 individual Count The first n That's ok ( from 0 Numbered starting ) The numbers are n+1 term , front n All lines have \frac{n(n+1)}{2} Number The first n That's ok ( from 0 open beginning Ed Number ) Count word Yes n+1 term , front n That's ok common Yes 2n(n+1) individual Count
- The first n That's ok Of The first m individual Count ( from 0 open beginning Ed Number ) can surface in by Group close Count C n m = n ! m ! ( n − m ) ! The first n OK, No m Number ( from 0 Numbered starting ) Can be expressed as a combined number \mathrm{C}_n^m = \frac{n!}{m!(n-m)!} The first n That's ok Of The first m individual Count ( from 0 open beginning Ed Number ) can surface in by Group close Count Cnm=m!(n−m)!n!
- Each number is equal to the sum of the left and right numbers in the previous line
- ( a + b ) n Of exhibition open type ( Two term type exhibition open ) in Of various term system Count In accordance with the Time Yes Should be Yang Brightness 3、 ... and horn The first n That's ok in Of Every time One term ( Such as : ( a + b ) 2 = a 2 + 2 a b + b 2 ) \ (a+b)^n The expansion of ( Binomial expansion ) The coefficients in correspond to Yang Hui triangle n Each item in the line ( Such as : \ (a+b)^2 = a^2 + 2ab + b^2) (a+b)n Of exhibition open type ( Two term type exhibition open ) in Of various term system Count In accordance with the Time Yes Should be Yang Brightness 3、 ... and horn The first n That's ok in Of Every time One term ( Such as : (a+b)2=a2+2ab+b2)
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