A354011
Number of tilings of a 3 X n rectangle using 2 X 2 tiles, right trominoes and dominoes.
Original entry on oeis.org
1, 0, 7, 8, 81, 184, 1051, 3176, 14609, 50408, 210903, 773888, 3102369, 11711856, 46045259, 176114128, 686258465, 2640610128, 10247733223, 39540368248, 153162778865, 591718044968, 2290106238779, 8852558325048, 34248315785777, 132424316290104, 512224146701367
Offset: 0
a(2)=7:
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A354012
Number of tilings of a 4 X n rectangle using 2 X 2 tiles, right trominoes and dominoes.
Original entry on oeis.org
1, 1, 17, 81, 702, 4623, 35044, 248045, 1819731, 13110984, 95362462, 690253391, 5008926698, 36300216768, 263252448712, 1908449014617, 13837881924141, 100326715619679, 727420462629671, 5274035027493046, 38238994112367061, 277246970248002472, 2010151423463689959
Offset: 0
a(2)=17, mirroring included (h: horizontal, v: vertical):
v v h,v v h
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2 + 2 + 1 + 4 + 1 + 1 + 1 + 2 + 1 + 2 = 17.
- Index entries for linear recurrences with constant coefficients, signature (5,28,-69,-142,194,78,-57,-36,70,-32).
A354130
Triangle read by rows: T(k,n) (k >= 0, n = 0, ..., k) = number of tilings of a k X n rectangle using 2 X 2, and 1 X 1 tiles, right trominoes and dominoes.
Original entry on oeis.org
1, 1, 1, 1, 2, 12, 1, 3, 48, 405, 1, 5, 216, 4185, 103300, 1, 8, 936, 40320, 2352830, 124098498, 1, 13, 4104, 397755, 55004286, 6763987198, 863829618636, 1, 21, 17928, 3892293, 1274945897, 364713815832, 108969107997657, 32100965172272499
Offset: 0
Triangle begins
k\n_0__1____2______3________4__________5____________6
0: 1
1: 1 1
2: 1 2 12
3: 1 3 48 405
4: 1 5 216 4185 103300
5: 1 8 936 40320 2352830 124098498
6: 1 13 4104 397755 55004286 6763987198 863829618636
A354131
Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.
Original entry on oeis.org
1, 2, 12, 48, 216, 936, 4104, 17928, 78408, 342792, 1498824, 6553224, 28652616, 125277192, 547747272, 2394904968, 10471198536, 45783025416, 200176267464, 875226954888, 3826738469448, 16731577137672, 73155162229704, 319854949515144, 1398495821923656
Offset: 0
a(3)=48
Number of tilings without a 2 X 2 square: 44, see A353878.
Number of other tilings: 4
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A354132
Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.
Original entry on oeis.org
1, 3, 48, 405, 4185, 40320, 397755, 3892293, 38193444, 374425263, 3671810235, 36003770640, 353046480345, 3461866214283, 33946152068808, 332866572321933, 3263999126947497, 32005882711563552, 313840950402409011, 3077438640586986141, 30176522977460549436
Offset: 0
a(2) = 48, see 2 X 3, A354131.
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