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A359021
Number of inequivalent tilings of a 5 X n rectangle using integer-sided square tiles.
10
1, 1, 5, 10, 39, 77, 521, 1985, 8038, 32097, 130125, 525676, 2131557, 8635656, 35017970, 141968455, 575692056, 2334344849, 9465939422, 38384559168, 155652202456, 631178976378, 2559476952229, 10378857744374, 42087027204278, 170665938023137, 692062856184512
OFFSET
0,3
FORMULA
For even n > 5:
a(n) = (A054857(n) + A079975(n) + 2*A054857(n/2) + 2* fixed_md(n/2) + 2*A054857((n-4)/2) + 4*A054857((n-2)/2) + 2* (A054857((n/2)-1) + fixed_md((n/2)-1)))/4.
For odd n > 5:
a(n) = (A054857(n) + A079975(n) + 2*A054857((n-1)/2) + 4*A054857((n-3)/2) + 2*fixed_md((n-3)/2) + 2*A054857((n-5)/2) + 2*fixed_md((n-1)/2))/4.
where
fixed_md(1)=1, fixed_md(2)=3, fixed_md(3)=15 and for n > 3, fixed_md(n) = A054857(n-1) + A054857(n-2) + fixed_md(n-2)+ fixed_md(n-1) + 2*A054857(n-3) + fixed_md(n-3).
EXAMPLE
a(2) is 5 because of:
+-+-+ +-+-+ +-+-+ +-+-+ +-+-+
| | | | | | | | | | |
+-+-+ +-+-+ + + + + +-+-+
| | | | | | | | | | |
+-+-+ + + +-+-+ +-+-+ + +
| | | | | | | | | | | |
+-+-+ +-+-+ +-+-+ +-+-+ +-+-+
| | | | | | | | | | | | |
+-+-+ + + + + +-+-+ +-+-+
| | | | | | | | | | | | |
+-+-+ +-+-+ +-+-+ +-+-+ +-+-+
CROSSREFS
Column k = 5 of A227690.
Sequences for fixed and free (inequivalent) tilings of m X n rectangles, for 2 <= m <= 10:
Cf. A079975.
Sequence in context: A271604 A365690 A277816 * A355327 A279764 A191580
KEYWORD
nonn
AUTHOR
John Mason, Dec 12 2022
STATUS
approved