A368258 - OEIS

A368258

Table read by downward antidiagonals: T(n,k) is the number of tilings of the n X k cylinder up to horizontal reflections by two tiles that are each fixed under horizontal reflection.

2, 4, 3, 8, 10, 4, 16, 36, 20, 6, 32, 136, 120, 55, 8, 64, 528, 816, 666, 136, 13, 128, 2080, 5984, 9316, 3536, 430, 18, 256, 8256, 45760, 139656, 106912, 23052, 1300, 30, 512, 32896, 357760, 2164240, 3371840, 1415896, 151848, 4435, 46

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

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 20 120 816 5984 45760

4 | 6 55 666 9316 139656 2164240

5 | 8 136 3536 106912 3371840 107505280

6 | 13 430 23052 1415896 89751728 5730905440

7 | 18 1300 151848 19206736 2454791328 314154568000

MATHEMATICA

A368258[n_, m_] := 1/(2n)*(DivisorSum[n, EulerPhi[#]*2^(n*m/#)&] + n*2^(n*m/2)*If[EvenQ[n], 1/2*(2^m + 1), 2^(m/2)])

CROSSREFS

Sequence in context: A241909 A245451 A371183 * A368264 A026166 A186003

Adjacent sequences: A368255 A368256 A368257 * A368259 A368260 A368261

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Dec 21 2023

STATUS

approved