A368264 Table read by downward antidiagonals: T(n,k) is the number of tilings of the n X k cylinder by two distinct tiles.

2, 4, 3, 8, 10, 4, 16, 36, 24, 6, 32, 136, 176, 70, 8, 64, 528, 1376, 1044, 208, 14, 128, 2080, 10944, 16456, 6560, 700, 20, 256, 8256, 87424, 262416, 209728, 43800, 2344, 36, 512, 32896, 699136, 4195360, 6710912, 2796976, 299600, 8230, 60

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Peter Kagey, Illustration of T(2,3)=36

Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023.

Example

Table begins:
  n\k|  1   2     3       4         5           6
  ---+-------------------------------------------
   1 |  2   4     8      16        32          64
   2 |  3  10    36     136       528        2080
   3 |  4  24   176    1376     10944       87424
   4 |  6  70  1044   16456    262416     4195360
   5 |  8 208  6560  209728   6710912   214748416
   6 | 14 700 43800 2796976 178962784 11453291200

Mathematica

A368264[n_, m_] := 1/n (DivisorSum[n, EulerPhi[#]*2^(n*m/#) &])

Crossrefs

Cf. A117401, A368257, A368259, A368261, A368263.

Sequence in context: A245451 A371183 A368258 * A026166 A186003 A377835

Adjacent sequences: A368261 A368262 A368263 * A368265 A368266 A368267

Keyword

nonn,tabl

Author

Peter Kagey, Dec 21 2023

Status

approved