$$5$$

$$7$$

$$8$$

$$13$$

$${x_n} = 2{x_{n - 1}}$$

$${x_n} = {x_{\left[ {n/2} \right]}} + 1$$

$${x_n} = {x_{\left[ {n/2} \right]}} + n$$

$${x_n} = {x_{n - 1}} + {x_{n - 2}}$$

$$27$$

$$28$$

$$29$$

$$30$$

$${{\left( {n + b - 1} \right)!\left( {n + r - 1} \right)!} \over {\left( {n - 1} \right)!b!\left( {n - 1} \right)!r!}}$$

$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {\left( {n - 1} \right)!\left( {n - 1} \right)!\left( {b + r} \right)!}}$$

$${{n!} \over {b!r!}}$$

$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {n!\left( {b + r - 1} \right)!}}$$