OFFSET
0,3
LINKS
John Mason, Table of n, a(n) for n = 0..1000
John Mason, Counting free tilings of a rectangle
FORMULA
For even n > 4
2 * Sum_{k=0..(n - 2) / 2} (A054856(k))) / 4
For odd n > 4
Where compo(n) is the number of distinct compositions of n as a sum of 1, 2, (1+1) and 4.
EXAMPLE
a(3) is 6 because of:
+-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+
| | | | | | | | | | | | | | | | | | |
+-+-+-+ + + + +-+ + +-+ + +-+ +-+-+-+
| | | | | | | | | | | | | | | | | |
+-+-+-+ + + +-+-+-+ +-+-+-+ +-+-+-+ + +-+
| | | | | | | | | | | | | | | | | | |
+-+-+-+ +-+-+-+ + +-+ +-+ + +-+-+-+ +-+-+-+
| | | | | | | | | | | | | | | | | | | |
+-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+ +-+-+-+
CROSSREFS
Column k = 4 of A227690.
Sequences for fixed and free (inequivalent) tilings of m X n rectangles, for 2 <= m <= 10:
KEYWORD
nonn
AUTHOR
John Mason, Dec 12 2022
STATUS
approved