A323423 Number of tilings of a 12 X n rectangle using 2*n copies of the disconnected shape [ooo___ooo].

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

Alois P. Heinz, Table of n, a(n) for n = 0..4893

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:
.
   ._._._._._._._._._.   ._____._._._._____.   ._._._._._._._._._.
   | | | | | | | | | |   |_____| | | |_____|   | | | | | | | | | |
   | | | | | | | | | |   |_____| | | |_____|   | | | | | | | | | |
   |_|_|_|_|_|_|_|_|_|   |_____|_|_|_|_____|   |_|_|_|_|_|_|_|_|_|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   |_|_|_|_|_|_|_|_|_|   |_____|_|_|_|_____|   |_____|_|_|_|_____|
   | | | | | | | | | |   |_____| | | |_____|   | | | | | | | | | |
   | | | | | | | | | |   |_____| | | |_____|   | | | | | | | | | |
   |_|_|_|_|_|_|_|_|_|   |_____|_|_|_|_____|   |_|_|_|_|_|_|_|_|_|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   |_|_|_|_|_|_|_|_|_|   |_____|_|_|_|_____|   |_____|_|_|_|_____|
.
   ._____._._._._____.   ._____._._._._____.   ._____._._._._____.
   |_____| | | |_____|   |_____| | | |_____|   |_____| | | |_____|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   | | | |_|_|_| | | |   | | | |_|_|_| | | |   |_____|_|_|_|_____|
   |_|_|_| | | |_|_|_|   | | | | | | | | | |   | | | | | | | | | |
   |_____| | | |_____|   |_|_|_| | | |_|_|_|   | | | | | | | | | |
   |_____|_|_|_|_____|   |_____|_|_|_|_____|   |_|_|_|_|_|_|_|_|_|
   |_____| | | |_____|   |_____| | | |_____|   |_____| | | |_____|
   | | | | | | | | | |   |_____| | | |_____|   |_____| | | |_____|
   | | | |_|_|_| | | |   | | | |_|_|_| | | |   |_____|_|_|_|_____|
   |_|_|_| | | |_|_|_|   | | | | | | | | | |   | | | | | | | | | |
   |_____| | | |_____|   |_|_|_| | | |_|_|_|   | | | | | | | | | |
   |_____|_|_|_|_____|   |_____|_|_|_|_____|   |_|_|_|_|_|_|_|_|_|
.

Crossrefs

Cf. A320437, A323352, A323483, A322473.

Sequence in context: A036707 A054311 A183452 * A236577 A356091 A359351

Adjacent sequences: A323420 A323421 A323422 * A323424 A323425 A323426

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 14 2019

Status

approved