A323352 Number of tilings of an 8 X n rectangle using 2*n copies of the disconnected shape [oo__oo].

1, 1, 1, 1, 1, 1, 5, 11, 36, 69, 112, 163, 260, 425, 897, 1845, 3910, 7524, 13683, 23675, 41741, 74882, 141758, 272059, 525251, 992342, 1841482, 3361173, 6142594, 11291891, 21037446, 39459473, 74198937, 138852912, 258417206, 478462336, 885161178, 1640011925

Offset

0,7

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..3712

Alois P. Heinz, G.f. for A323352

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

G.f.: see link above.

a(n) ~ c * d^n, where d = 1.860082974490657614690253062429801614977133563402428780098509287692125963... and c = 0.175453010088369049748675582204204705345337476531410983285862441563015... - Vaclav Kotesovec, Jan 15 2019

Example

a(6) = 5:
.
   ._._._._._._.    .___._._.___.    .___._._.___.
   | | | | | | |    |___| | |___|    |___| | |___|
   |_|_|_|_|_|_|    |___|_|_|___|    |___|_|_|___|
   | | | | | | |    |___| | |___|    | | | | | | |
   |_|_|_|_|_|_|    |___|_|_|___|    |_|_|_|_|_|_|
   | | | | | | |    |___| | |___|    |___| | |___|
   |_|_|_|_|_|_|    |___|_|_|___|    |___|_|_|___|
   | | | | | | |    |___| | |___|    | | | | | | |
   |_|_|_|_|_|_|    |___|_|_|___|    |_|_|_|_|_|_|
.
   ._._._._._._.    .___._._.___.
   | | | | | | |    |___| | |___|
   |_|_|_|_|_|_|    | | |_|_| | |
   |___| | |___|    |_|_| | |_|_|
   |___|_|_|___|    |___|_|_|___|
   | | | | | | |    |___| | |___|
   |_|_|_|_|_|_|    | | |_|_| | |
   |___| | |___|    |_|_| | |_|_|
   |___|_|_|___|    |___|_|_|___|
.

Crossrefs

Cf. A320437, A323423, A323483, A322473.

Sequence in context: A164560 A054854 A188161 * A005178 A065315 A065317

Adjacent sequences: A323349 A323350 A323351 * A323353 A323354 A323355

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 12 2019

Status

approved