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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

REFERENCES

D. E. Knuth: The Art of Computer Programming, Volume 4, Pre-fascicle 5C, Dancing Links, 2018.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3000

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

Cf. A323352, A323423, A323483, A322473.

Sequence in context: A228616 A151670 A153587 * A059286 A076998 A173956

Adjacent sequences:  A320434 A320435 A320436 * A320438 A320439 A320440

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 08 2019

STATUS

approved

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Last modified January 26 05:40 EST 2020. Contains 331273 sequences. (Running on oeis4.)