login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of tilings of a 12 X n rectangle using 2*n copies of the disconnected shape [ooo___ooo].
5

%I #26 Nov 15 2023 17:40:14

%S 1,1,1,1,1,1,1,1,1,6,13,22,64,114,172,242,320,406,561,811,1188,2204,

%T 4093,7181,13185,22687,36597,56934,85897,126485,189500,290730,453035,

%U 739070,1234480,2061104,3452517,5710991,9253861,14755851,23232374,36208272,56484574

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

%H Alois P. Heinz, <a href="/A323423/b323423.txt">Table of n, a(n) for n = 0..4893</a>

%H D. E. Knuth, <a href="https://www.youtube.com/watch?v=_cR9zDlvP88">Dancing Links</a>, 24th Annual Christmas Lecture, Stanfordonline video (2018)

%H D. E. Knuth, <a href="https://arxiv.org/abs/cs/0011047">Dancing Links</a>, arXiv:cs/0011047 [cs.DS], 2000.

%H Vaclav Kotesovec, <a href="/A323423/a323423.txt">G.f. for A323423</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dancing_Links">Dancing Links</a>

%F a(n) ~ c * d^n, where d = 1.6015104441944202301254108408823287548000767754983674455370068394906003425... and c = 0.146413500304969675060082381912654288970333957537812034040245936... - _Vaclav Kotesovec_, Jan 15 2019

%e a(9) = 6:

%e .

%e ._._._._._._._._._. ._____._._._._____. ._._._._._._._._._.

%e | | | | | | | | | | |_____| | | |_____| | | | | | | | | | |

%e | | | | | | | | | | |_____| | | |_____| | | | | | | | | | |

%e |_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e |_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_____|_|_|_|_____|

%e | | | | | | | | | | |_____| | | |_____| | | | | | | | | | |

%e | | | | | | | | | | |_____| | | |_____| | | | | | | | | | |

%e |_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e |_|_|_|_|_|_|_|_|_| |_____|_|_|_|_____| |_____|_|_|_|_____|

%e .

%e ._____._._._._____. ._____._._._._____. ._____._._._._____.

%e |_____| | | |_____| |_____| | | |_____| |_____| | | |_____|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e | | | |_|_|_| | | | | | | |_|_|_| | | | |_____|_|_|_|_____|

%e |_|_|_| | | |_|_|_| | | | | | | | | | | | | | | | | | | | |

%e |_____| | | |_____| |_|_|_| | | |_|_|_| | | | | | | | | | |

%e |_____|_|_|_|_____| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|

%e |_____| | | |_____| |_____| | | |_____| |_____| | | |_____|

%e | | | | | | | | | | |_____| | | |_____| |_____| | | |_____|

%e | | | |_|_|_| | | | | | | |_|_|_| | | | |_____|_|_|_|_____|

%e |_|_|_| | | |_|_|_| | | | | | | | | | | | | | | | | | | | |

%e |_____| | | |_____| |_|_|_| | | |_|_|_| | | | | | | | | | |

%e |_____|_|_|_|_____| |_____|_|_|_|_____| |_|_|_|_|_|_|_|_|_|

%e .

%Y Cf. A320437, A323352, A323483, A322473.

%K nonn,easy

%O 0,10

%A _Alois P. Heinz_, Jan 14 2019