No.287 Number of Combinations
tekitouk
問題文最終更新日: 2026-06-26 06:07:10
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yukicoder contest 122
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Problem Statement
Let $n$ be an integer greater than or equal to $1$.
Find the number $G(n)$ of tuples of integers $(a,b,c,d,e,f,g,h)$ that satisfy $a+b+c+d+e+f+g+h=6n$ and also satisfy
$0 \le a \le n,$
$0 \le b \le n,$
$0 \le c \le n,$
$0 \le d \le n,$
$0 \le e \le n,$
$0 \le f \le n,$
$0 \le g \le n,$
$0 \le h \le n$
.
Input
$n$
The input is given as an integer.
$1 \le n \le 100$
Output
Print a newline at the end.
Output $G(n)$.
Sample
Sample 1
Input
1
Output
28
There are two 0s and six 1s, so there are ${}_{8}{\rm C}_{2}=28$ ways.
Sample 2
Input
10
Output
796510
Sample 3
Input
100
Output
2721355068691
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