-1
votes
1answer
80 views

Count the number of integer solution to $\sum_{i=1}^ {4}{a_i\times b_i} \geq 8 $? [closed]

Count the number of integer solution to $\sum_{i=1}^ {4}{a_i\times b_i} \geq 8 $ such that condition 1: $1 \leq a_i \leq 7$ condition 2: $1 \leq b_i \leq 4$ condition 3: $\sum_{i=1}^{4} {a_i} = ...
0
votes
1answer
109 views

Count the number of integer solution to $\sum_{i=1}^ {2}{a_i\times b_i} \geq 6 $ [closed]

Count the number of integer solution to $\sum_{i=1}^ {2}{a_i\times b_i} \geq 6 $ such that condition 1: $1 \leq a_i \leq 7$ condition 2: $1 \leq b_i \leq 4$ condition 3: $\sum_{i=1}^{2} {a_i} = 8$ ...
18
votes
3answers
477 views

An Inequality Involving Bell Numbers: $B_n^2 \leq B_{n-1}B_{n+1}$

The following inequality came up while trying to resolve a conjecture about a certain class of partitions (the context is not particularly enlightening): $$ B_n^2 \leq B_{n-1}B_{n+1} $$ for $n \geq ...