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A320437
Number of tilings of a 12 X n rectangle using 3*n copies of the disconnected shape [o_oo_o].
5
1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 12, 22, 26, 10, 58, 218, 314, 218, 726, 2286, 3434, 2678, 9766, 30962, 45680, 40640, 148162, 468338, 689264, 683498, 2518026, 7794088, 11554876, 12462092, 45335614, 137227934, 206599268, 239436918, 843541244
OFFSET
0,8
REFERENCES
D. E. Knuth: The Art of Computer Programming, Volume 4, Pre-fascicle 5C, Dancing Links, 2018.
LINKS
D. E. Knuth, Dancing Links, 24th Annual Christmas Lecture, Stanfordonline video (2018)
D. E. Knuth, Dancing Links, arXiv:cs/0011047 [cs.DS], 2000.
Wikipedia, Dancing Links
FORMULA
a(n) > 0 for n >= 11.
a(n) == 0 (mod 2) for n >= 1.
EXAMPLE
a(7) = 2:
.
1234567 1234567
+-----------+-----------+
1 : ABAACAD : DACAABA :
2 : EFGFFHF : FHFFGFE :
3 : IBIICID : DICIIBI :
4 : EBGJCHD : DHCJGBE :
5 : EKGKKHK : KHKKGKE :
6 : LBMJCND : DNCJMBL :
7 : EOGJPHQ : QHPJGOE :
8 : LRMRRNR : RNRRMRL :
9 : LOMJPNQ : QNPJMOL :
10 : SOSSPSQ : QSPSSOS :
11 : LTMTTNT : TNTTMTL :
12 : UOUUPUQ : QUPUUOU :
.
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 08 2019
STATUS
approved