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A323423
Number of tilings of a 12 X n rectangle using 2*n copies of the disconnected shape [ooo___ooo].
5
1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 13, 22, 64, 114, 172, 242, 320, 406, 561, 811, 1188, 2204, 4093, 7181, 13185, 22687, 36597, 56934, 85897, 126485, 189500, 290730, 453035, 739070, 1234480, 2061104, 3452517, 5710991, 9253861, 14755851, 23232374, 36208272, 56484574
OFFSET
0,10
LINKS
D. E. Knuth, Dancing Links, 24th Annual Christmas Lecture, Stanfordonline video (2018)
D. E. Knuth, Dancing Links, arXiv:cs/0011047 [cs.DS], 2000.
Vaclav Kotesovec, G.f. for A323423
Wikipedia, Dancing Links
FORMULA
a(n) ~ c * d^n, where d = 1.6015104441944202301254108408823287548000767754983674455370068394906003425... and c = 0.146413500304969675060082381912654288970333957537812034040245936... - Vaclav Kotesovec, Jan 15 2019
EXAMPLE
a(9) = 6:
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._._._._._._._._._. ._____._._._._____. ._._._._._._._._._.
| | | | | | | | | | |_____| | | |_____| | | | | | | | | | |
| | | | | | | | | | |_____| | | |_____| | | | | | | | | | |
|_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
|_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_____|_|_|_|_____|
| | | | | | | | | | |_____| | | |_____| | | | | | | | | | |
| | | | | | | | | | |_____| | | |_____| | | | | | | | | | |
|_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
|_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_____|_|_|_|_____|
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._____._._._._____. ._____._._._._____. ._____._._._._____.
|_____| | | |_____| |_____| | | |_____| |_____| | | |_____|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
| | | |_|_|_| | | | | | | |_|_|_| | | | |_____|_|_|_|_____|
|_|_|_| | | |_|_|_| | | | | | | | | | | | | | | | | | | | |
|_____| | | |_____| |_|_|_| | | |_|_|_| | | | | | | | | | |
|_____|_|_|_|_____| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|
|_____| | | |_____| |_____| | | |_____| |_____| | | |_____|
| | | | | | | | | | |_____| | | |_____| |_____| | | |_____|
| | | |_|_|_| | | | | | | |_|_|_| | | | |_____|_|_|_|_____|
|_|_|_| | | |_|_|_| | | | | | | | | | | | | | | | | | | | |
|_____| | | |_____| |_|_|_| | | |_|_|_| | | | | | | | | | |
|_____|_|_|_|_____| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|
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CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jan 14 2019
STATUS
approved