cp's OEIS Frontend

a(n) is the number of ways to tile a zig-zag strip of n cells using squares (of length 1), strips (of length 3), and triangles (using 3 cells), where the zig-zag strip begins below the center line. Here is the zig-zag strip corresponding to n=12, with 12 cells:

_ _ _

| | | | | |

| _| |_ | _| |_

| | | | | | |

|__|___|_|___| |___|

| | | | | |

|_| |_| |_|,

and here are the three possible triangles and strips (which can also be rotated or reflected):

_

| |

| | _

| | | |

| _| _ ___ _ | |

| | | | | |

|_|, |_ ___ _|, |_ ___|.

As an example, here is one of the a(12) = 86 ways to tile the skew double-strip of 12 cells:

_ _ _

| | | | | |

| |___| |___|_|_

| | | |

| _|_ |__________|

| | | | | |

|_| |_| |_|.