A square is divided into three equal parts horizontally to create [Figure 1], and divided into three equal parts vertically to create [Figure 2]. [Figure 1] and [Figure 2] are alternately attached repeatedly to create the following figure. As shown in the figure, let A be the upper left vertex of the first attached [Figure 1], and let $\mathrm { B } _ { n }$ be the lower right vertex of the figure created by attaching a total of $n$ figures (combining the number of [Figure 1] and [Figure 2]). When $a _ { n }$ is the number of shortest paths from vertex A to vertex $\mathrm { B } _ { n }$ along the lines, what is the value of $a _ { 3 } + a _ { 7 }$? [4 points] (1) 26 (2) 28 (3) 30 (4) 32 (5) 34
A square is divided into three equal parts horizontally to create [Figure 1], and divided into three equal parts vertically to create [Figure 2]. [Figure 1] and [Figure 2] are alternately attached repeatedly to create the following figure. As shown in the figure, let A be the upper left vertex of the first attached [Figure 1], and let $\mathrm { B } _ { n }$ be the lower right vertex of the figure created by attaching a total of $n$ figures (combining the number of [Figure 1] and [Figure 2]).
When $a _ { n }$ is the number of shortest paths from vertex A to vertex $\mathrm { B } _ { n }$ along the lines, what is the value of $a _ { 3 } + a _ { 7 }$? [4 points]\\
(1) 26\\
(2) 28\\
(3) 30\\
(4) 32\\
(5) 34