A219987 -id:A219987 - cp's OEIS frontend

A052980 Expansion of (1 - x)/(1 - 2*x - x^3).

1, 1, 2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, 1914332891, 4222194104, 9312342245, 20539017381, 45300228866

Offset: 0

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

a(n) counts permutations of length n which embed into the (infinite) increasing oscillating sequence given by 4,1,6,3,8,5,...,2k+2,2k-1,...; these are also the permutations which avoid {321, 2341, 3412, 4123}. - Vincent Vatter, May 23 2008
a(n) is the top left entry of the n-th power of any of the 3X3 matrices [1, 1, 0; 1, 1, 1; 1, 0, 0] or [1, 1, 1; 1, 1, 0; 0, 1, 0] or [1, 1, 1; 0, 0, 1; 1, 0, 1] or [1, 0, 1; 1, 0, 0; 1, 1, 1]. - R. J. Mathar, Feb 03 2014
a(n) is the number of possible tilings of a 2 X n board, using dominoes and L-shaped trominoes. - Michael Tulskikh, Aug 21 2019
a(n) = A190512(n-1) for n>0. - Greg Dresden, Feb 28 2020

Kenneth Edwards and Michael A. Allen, A new combinatorial interpretation of the Fibonacci numbers squared, Part II, Fib. Q., 58:2 (2020), 169-177.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Kassie Archer and Noel Bourne, Pattern avoidance in compositions and powers of permutations, arXiv:2505.05218 [math.CO], 2025. See p. 4.
Robert Brignall, Nik Ruškuc, and Vincent Vatter, Simple permutations: decidability and unavoidable substructures, Theoretical Computer Science 391 (2008), 150-163.
Greg Dresden and Michael Tulskikh, Tilings of 2 X n boards with dominos and L-shaped trominos, Washington & Lee University (2021).
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1053
Djamila Oudrar, Sur l'énumération de structures discrètes, une approche par la théorie des relations, Thesis (in French), arXiv:1604.05839 [math.CO], 2016.
Djamila Oudrar and Maurice Pouzet, Profile and hereditary classes of ordered relational structures, arXiv preprint arXiv:1409.1108 [math.CO], 2014 [The first version of this document erroneously gives the A-number as A005298]
Vincent Vatter, Small permutation classes, arXiv:0712.4006 [math.CO], 2007-2016.
Index entries for linear recurrences with constant coefficients, signature (2,0,1).

See A190512 and A110513 for other versions of this sequence.
Column k=2 of A219987.
Cf. A008998.

I:=[1,1,2]; [n le 3 select I[n] else 2*Self(n-1)+Self(n-3): n in [1..40]];

R:=PowerSeriesRing(Integers(), 32); Coefficients(R!( (1 - x)/(1 - 2*x - x^3))); // Marius A. Burtea, Feb 14 2020

spec := [S,{S=Sequence(Prod(Union(Prod(Z,Z,Z),Z),Sequence(Z)))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);

CoefficientList[Series[(1 - x)/(1 - 2 x - x^3), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 05 2014 *)

Vec((1-x)/(1-2*x-x^3)+O(x^99)) \\ Charles R Greathouse IV, Nov 20 2011

Recurrence: a(0)=1, a(1)=1, a(2)=2; thereafter a(n) = 2*a(n-1)+a(n-3).
a(n) = Sum(1/59*(4+3*_alpha^2+17*_alpha)*_alpha^(-1-n), _alpha = RootOf(-1+2*_Z+_Z^3)).
a(n) = A008998(n) - A008998(n-1). - R. J. Mathar, Feb 04 2014
Let u1 = 2.20556943... denote the real root of x^3-2*x^2-1. There is an explicit constant c1 = 0.460719842... such that for n>0, a(n) = nearest integer to c1*u1^n. - N. J. A. Sloane, Nov 07 2016
a(2n) = a(n)^2 - a(n-1)^2 + (1/2)*(a(n+2) - a(n+1) - a(n))^2. - Greg Dresden and Michael Tulskikh, Aug 20 2019
a(n) = 2^(n-1) + Sum_{i=3..n}(2^(n-i)*a(i-3)). - Greg Dresden, Aug 27 2019
a(n+1) = (Sum_{i >= 0} 2^(n-3i-2)*(4*binomial(n-2i, i) + binomial(n-2i-2, i))). - Michael Tulskikh, Feb 14 2020
a(n) = A008998(n-1) + A008998(n-3). - Michael Tulskikh, Feb 14 2020

A219866 Number A(n,k) of tilings of a k X n rectangle using dominoes and straight (3 X 1) trominoes; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 2, 7, 14, 7, 2, 1, 1, 2, 15, 41, 41, 15, 2, 1, 1, 3, 30, 143, 184, 143, 30, 3, 1, 1, 4, 60, 472, 1069, 1069, 472, 60, 4, 1, 1, 5, 123, 1562, 5624, 9612, 5624, 1562, 123, 5, 1

Offset: 0

Alois P. Heinz, Nov 30 2012

			A(2,3) = A(3,2) = 4, because there are 4 tilings of a 3 X 2 rectangle using dominoes and straight (3 X 1) trominoes:
  .___.   .___.   .___.   .___.
  | | |   |___|   | | |   |___|
  | | |   |___|   |_|_|   | | |
  |_|_|   |___|   |___|   |_|_|
Square array A(n,k) begins:
  1,  1,  1,    1,     1,      1,        1,         1, ...
  1,  0,  1,    1,     1,      2,        2,         3, ...
  1,  1,  2,    4,     7,     15,       30,        60, ...
  1,  1,  4,   14,    41,    143,      472,      1562, ...
  1,  1,  7,   41,   184,   1069,     5624,     29907, ...
  1,  2, 15,  143,  1069,   9612,    82634,    707903, ...
  1,  2, 30,  472,  5624,  82634,  1143834,  15859323, ...
  1,  3, 60, 1562, 29907, 707903, 15859323, 354859954, ...

Liang Kai, Antidiagonals n = 0..35, flattened (0..22 from Alois P. Heinz)
Kai Liang, Solving tiling enumeration problems by tensor network contractions, arXiv:2503.17698 [math.CO], 2025. See p. 25, Table 4.

Columns (or rows) k=0-10 give: A000012, A000931(n+3), A129682, A219867, A219862, A219868, A219869, A219870, A219871, A219872, A219873.
Main diagonal gives: A219874.
Cf. A219987, A364457.

b:= proc(n, l) option remember; local k, t;
      if max(l[])>n then 0 elif n=0 or l=[] then 1
    elif min(l[])>0 then t:=min(l[]); b(n-t, map(h->h-t, l))
    else for k do if l[k]=0 then break fi od;
         b(n, subsop(k=3, l))+ b(n, subsop(k=2, l))+
         `if`(k `if`(n>=k, b(n, [0$k]), b(k, [0$n])):
seq(seq(A(n, d-n), n=0..d), d=0..10);

b[n_, l_] := b[n, l] = Module[{k, t}, If [Max[l] > n, 0, If[ n == 0 || l == {}, 1, If[Min[l] > 0, t = Min[l]; b[n-t, l-t], k = Position[l, 0, 1][[1, 1]]; b[n, ReplacePart[l, k -> 3]] + b[n, ReplacePart[l, k -> 2]] + If[k < Length[l] && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[k+1 < Length[l] && l[[k+1]] == 0 && l[[k+2]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1, k+2 -> 1}]], 0]]]]]; a[n_, k_] := If[n >= k, b[n, Array[0&, k]], b[k, Array[0&, n]]]; Table[Table[a[n, d-n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Dec 16 2013, translated from Maple *)

A364457 Number A(n,k) of tilings of a k X n rectangle using dominoes and trominoes (of any shape); square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 6, 6, 1, 1, 1, 2, 17, 30, 17, 2, 1, 1, 2, 43, 145, 145, 43, 2, 1, 1, 3, 108, 733, 1352, 733, 108, 3, 1, 1, 4, 280, 3540, 12688, 12688, 3540, 280, 4, 1, 1, 5, 727, 17300, 115958, 226922, 115958, 17300, 727, 5, 1

Offset: 0

Alois P. Heinz, Jul 25 2023

			A(3,2) = A(2,3) = 6:
  .___.   .___.   .___.   .___.   .___.   .___.
  | | |   |___|   | | |   |___|   | ._|   |_. |
  | | |   |___|   |_|_|   | | |   |_| |   | |_|
  |_|_|   |___|   |___|   |_|_|   |___|   |___|  .
.
Square array A(n,k) begins:
  1, 1,   1,     1,       1,        1,          1,            1, ...
  1, 0,   1,     1,       1,        2,          2,            3, ...
  1, 1,   2,     6,      17,       43,        108,          280, ...
  1, 1,   6,    30,     145,      733,       3540,        17300, ...
  1, 1,  17,   145,    1352,    12688,     115958,      1075397, ...
  1, 2,  43,   733,   12688,   226922,    3927233,     68846551, ...
  1, 2, 108,  3540,  115958,  3927233,  128441094,   4263997124, ...
  1, 3, 280, 17300, 1075397, 68846551, 4263997124, 267855152858, ...

Alois P. Heinz, Table of n, a(n) for n = 0..350
Liang Kai, Solving tiling enumeration problems by tensor network contractions, arXiv:2503.17698 [math.CO], 2025.
Wikipedia, Domino (mathematics)
Wikipedia, Tromino

Columns (or rows) k=0-10 give: A000012, A182097(n) = A000931(n+3), A019439, A364460, A364155, A364556, A364616, A364617, A364632, A364638, A364640.
Main diagonal gives A364504.
Cf. A219866, A219987, A233320.

A(n,k) = A(k,n).

Terms n,k>=4 had to be corrected as was pointed out by Martin Fuller and David Radcliffe - Alois P. Heinz, Apr 05 2025

A165716 Number of tilings of a 3 X n rectangle using dominoes and right trominoes.

Original entry on oeis.org

1, 0, 5, 8, 55, 140, 633, 1984, 7827, 26676, 99621, 351080, 1283247, 4583580, 16611505, 59652624, 215457835, 775371268, 2796772765, 10073343672, 36315180295, 130843331180, 471599612393, 1699398816608, 6124635653443, 22071172760532, 79541846573973

Offset: 0

Alois P. Heinz, Sep 24 2009

			a(2) = 5, because there are 5 tilings of a 3 X 2 rectangle using dominoes and right trominoes:
.___. .___. ._._. .___. .___.
|___| |_._| | | | | ._| |_. |
|___| | | | |_|_| |_| | | |_|
|___| |_|_| |___| |___| |___|

Alois P. Heinz, Table of n, a(n) for n = 0..550
Index entries for linear recurrences with constant coefficients, signature (2,6,-4,11,2).

Column k=3 of A219987.

a:= n-> (Matrix([[55, 8, 5, 0, 1]]). Matrix(5, (i,j)-> if i=j-1 then 1 elif j=1 then [2, 6, -4, 11, 2][i] else 0 fi)^n)[1,5]: seq(a(n), n=0..25);

a[n_] := Last[{55, 8, 5, 0, 1} . MatrixPower[ Table[ Which[i == j - 1, 1, j == 1, {2, 6, -4, 11, 2}[[i]], True, 0], {i, 1, 5}, {j, 1, 5}], n]]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Jul 19 2012, translated from Maple *)
LinearRecurrence[{2,6,-4,11,2},{1,0,5,8,55},30] (* Harvey P. Dale, Mar 19 2013 *)

G.f.: (2*x^4 - 2*x^3 + x^2 + 2*x - 1) / (2*x^5 + 11*x^4 - 4*x^3 + 6*x^2 + 2*x - 1).

a(0)=1, a(1)=0, a(2)=5, a(3)=8, a(4)=55, a(n) = 2*a(n-1) + 6*a(n-2) - 4*a(n-3) + 11*a(n-4) + 2*a(n-5). - Harvey P. Dale, Mar 19 2013

A165791 Number of tilings of a 4 X n rectangle using dominoes and right trominoes.

Original entry on oeis.org

1, 1, 11, 55, 380, 2319, 15171, 96139, 619773, 3962734, 25445515, 163048957, 1045897075, 6705473761, 43001795070, 275730928993, 1768128097215, 11337760387473, 72702310606249, 466192677008538, 2989403530821497, 19169143325987983, 122919655766448729

Offset: 0

Alois P. Heinz, Sep 26 2009

			a(2) = 11, because there are 11 tilings of a 4 X 2 rectangle using dominoes and right trominoes:
  .___. .___. .___. ._._. ._._. .___. .___. .___. .___. .___. .___.
  |___| |___| |_._| | | | | | | |___| |___| | ._| |_. | | ._| |_. |
  |___| |_._| | | | |_|_| |_|_| | ._| |_. | |_| | | |_| |_| | | |_|
  |___| | | | |_|_| |___| | | | |_| | | |_| |___| |___| | |_| |_| |
  |___| |_|_| |___| |___| |_|_| |___| |___| |___| |___| |___| |___|  .

Alois P. Heinz, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (4, 21, -25, -65, -17, 24, -11, -15, 9).

Cf. A165716, A127870, A054854, A226322.

Column k=4 of A219987.

a:= n-> (Matrix([[619773, 96139, 15171, 2319, 380, 55, 11, 1, 1]]). Matrix(9, (i,j)-> if i=j-1 then 1 elif j=1 then [4, 21, -25, -65, -17, 24, -11, -15, 9][i] else 0 fi)^n)[1,9]: seq(a(n), n=0..25);

a[n_] := {619773, 96139, 15171, 2319, 380, 55, 11, 1, 1} . MatrixPower[ Table[ Which[i == j-1, 1, j == 1, {4, 21, -25, -65, -17, 24, -11, -15, 9}[[i]], True, 0], {i, 1, 9}, {j, 1, 9}], n] // Last; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 04 2013, translated and adapted from Alois P. Heinz's Maple program *)

G.f.: (2*x^8-5*x^7+2*x^6-x^5-19*x^4-15*x^3+14*x^2+3*x-1) / (9*x^9-15*x^8-11*x^7+24*x^6-17*x^5-65*x^4-25*x^3+21*x^2+4*x-1).

A219994 Number of tilings of an n X n square using dominoes and right trominoes.

Original entry on oeis.org

1, 0, 2, 8, 380, 21272, 5350806, 3238675344, 6652506271144, 38896105985522272, 711716770252031164458, 38776997923112110535353528, 6460929292946758939597712150496, 3245656750963660788826395580466708824, 4953412325525289651086730443567098343730966, 22873302288206466754758793232467436030071524731072

Offset: 0

Alois P. Heinz, Dec 02 2012

nonn

			a(3) = 8, because there are 8 tilings of a 3 X 3 square using dominoes and right trominoes:
  .___._.   .___._.   .___._.   .___._.
  |___| |   |___| |   |___| |   |_. | |
  | ._|_|   | | |_|   | |___|   | |_|_|
  |_|___|   |_|___|   |_|___|   |_|___|
  ._.___.   ._.___.   ._.___.   ._.___.
  | |___|   | | ._|   | |___|   | |___|
  |___| |   |_|_| |   |_|_. |   |_| | |
  |___|_|   |___|_|   |___|_|   |___|_|  .

Alois P. Heinz, Table of n, a(n) for n = 0..17
Kai Liang, Solving tiling enumeration problems by tensor network contractions, arXiv:2503.17698 [math.CO], 2025. See p. 25, Table 4.

Main diagonal of A219987.

Cf. A233807, A364504.

A353877 Triangle read by rows: T(n,k) = number of tilings of a n X k rectangle using right trominoes, dominoes and 1 X 1 tiles, n >= 0, k = 0..n.

Original entry on oeis.org

1, 1, 1, 1, 2, 11, 1, 3, 44, 369, 1, 5, 189, 3633, 83374, 1, 8, 798, 34002, 1817897, 90916452, 1, 13, 3383, 323293, 40220893, 4635661331, 546063639624, 1, 21, 14328, 3058623, 886130549, 235025597912, 63919977468729, 17259079054003609, 1, 34, 60697, 28982628, 19546906987, 11935601703140, 7495901454256347, 4669873251135795702, 2916019543694306398589

Offset: 0

Gerhard Kirchner, May 09 2022

Tiling algorithm, see A351322.

Reading the sequence {T(n,k)} for k>n, use T(k,n) instead of T(n,k).

			Triangle begins
n\k_0__1____2______3________4__________5____________6
0:  1
1:  1  1
2:  1  2   11
3:  1  3   44    369
4:  1  5  189   3633    83374
5:  1  8  798  34002  1817897   90916452
6:  1 13 3383 323293 40220893 4635661331 546063639624

Liang Kai, Rows n=0..17, flattened

Row/columns 0..4 are A000012, A000045(n+1), A110679, A353878, A353879.
Main diagonal is A353934.
Cf. A219987, A351322, A352589.

Maxima
```
See A352589.
```

A219988 Number of tilings of a 5 X n rectangle using dominoes and right trominoes.

Original entry on oeis.org

1, 0, 24, 140, 2319, 21272, 262191, 2746048, 31411948, 342302244, 3830482893, 42241878920, 469601959777, 5197411955932, 57664560160890, 638914582091712, 7084373947760105, 78520055192688696, 870480364546718647, 9649003719594586976, 106963676725852631636

Offset: 0

Alois P. Heinz, Dec 02 2012

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (6, 76, -182, -590, 2722, -6151, -1636, 17717, -15910, -482, 10814, -4832, -4330, -5915, 13616, -8422, 2920, -216, -20).

Column k=5 of A219987.

gf:= (2*x^18 +52*x^17 -358*x^16 +1396*x^15 -3682*x^14 +4644*x^13 -2629*x^12 -1426*x^11 +906*x^10 +4146*x^9 -2315*x^8 -2804*x^7 +4106*x^6 -1636*x^5 +245*x^4 +178*x^3 -52*x^2 -6*x +1) /
(20*x^19 +216*x^18 -2920*x^17 +8422*x^16 -13616*x^15 +5915*x^14 +4330*x^13 +4832*x^12 -10814*x^11 +482*x^10 +15910*x^9 -17717*x^8 +1636*x^7 +6151*x^6 -2722*x^5 +590*x^4 +182*x^3 -76*x^2 -6*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq (a(n), n=0..30);

G.f.: see Maple program.

A219989 Number of tilings of a 6 X n rectangle using dominoes and right trominoes.

Original entry on oeis.org

1, 1, 53, 633, 15171, 262191, 5350806, 100578811, 1973546988, 37873593799, 735394314429, 14191155767741, 274752269763958, 5310160930571538, 102725211030603178, 1986240719213420369, 38415016070710912599, 742863889918219971720, 14366465865750557446408

Offset: 0

Alois P. Heinz, Dec 02 2012

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (13, 198, -1268, -5078, 29776, -59713, 78279, 498954, 1798776, 561821, -20759881, -9444877, 11727284, 134747676, -130787555, 21043915, 112821018, 214359517, -815649290, -545218943, 1428249826, 341486785, -795173421, -179637116, 189274778, 114723369, -52063405, -16579985, 10066106, -2491759, -1460964, 106664, 83096, -3524).

Column k=6 of A219987.

gf:= (144*x^33 -16884*x^32 -172332*x^31 +37368*x^30 +1446802*x^29 +1843379*x^28 +3892967*x^27 -4330825*x^26 -7997135*x^25 +2597250*x^24 +20344704*x^23 +1683173*x^22 -102335065*x^21 -11071738*x^20
+108818264*x^19 +20558409*x^18 -23625389*x^17 -12070930*x^16 +22478862*x^15 -21548636*x^14 -14801976*x^13 +5193535*x^12 +6957072*x^11 +1167575*x^10 -1273601*x^9 -201269*x^8 -40977*x^7 +40180*x^6 -17860*x^5 +2794*x^4 +1014*x^3 -158*x^2 -12*x +1) /
(3524*x^34 -83096*x^33 -106664*x^32 +1460964*x^31 +2491759*x^30 -10066106*x^29 +16579985*x^28 +52063405*x^27 -114723369*x^26 -189274778*x^25 +179637116*x^24 +795173421*x^23 -341486785*x^22
-1428249826*x^21 +545218943*x^20 +815649290*x^19 -214359517*x^18 -112821018*x^17 -21043915*x^16 +130787555*x^15 -134747676*x^14 -11727284*x^13 +9444877*x^12 +20759881*x^11 -561821*x^10 -1798776*x^9 -498954*x^8 -78279*x^7 +59713*x^6 -29776*x^5 +5078*x^4 +1268*x^3 -198*x^2 -13*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq (a(n), n=0..30);

G.f.: see Maple program.

A219990 Number of tilings of a 7 X n rectangle using dominoes and right trominoes.

Original entry on oeis.org

1, 0, 117, 1984, 96139, 2746048, 100578811, 3238675344, 111496884663, 3704964324320, 125449223494157, 4205142104025144, 141722416759943105, 4762489676605782896, 160291284486676070239, 5390369708368427166312, 181353331398435867957049, 6099936611677114512527724

Offset: 0

Alois P. Heinz, Dec 02 2012

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..300
Vaclav Kotesovec, G.f. for A219990
Index entries for linear recurrences with constant coefficients, signature (16, 828, -4894, -129950, 938794, 3076050, -73254056, 421387662, 849120418, -13714442525, 30545493728, 14247793479, -434718686270, -107645686099, -1299668668124, 35772839257223, -35931151572218, -119742324469870, -78216388113118, 1299560070314604, 1695384887837968, -25717356362574307, 50034906477121890, 10984539052892183, -199056082381036950, 381880294522734602, -478812415872955104, 1074167100263519206, -1179118001816919606, -174464365325254476, 2263121403940087100, -7629116999653731671, 16803247405222769324, -22344349883539447498, -4000409234281186364, -1706838123391389358, 13090805659244841300, 61003711574632273267, -57770563416503518400, 46875462436502843417, 5466013676505127022, -105153829059235247366, -120388104859890694460, 186194603632741562421, 129437236988775243440, -205177320074449805604, 155777539607171964998, -70147759384372501785, -110875152336965128526, 119895950939565612691, -23617010427386852756, -394683463178827092, -7789531116648697390, 1361975286360726935, 4555495413222005656, -2334498777819868462, 241757533961242782, 92501547981895820, -19476665773899792, -1134607808488740, 115594985559448, -6099935845648, -754632052096, 1782882432).

Column k=7 of A219987.

G.f.: see link above. - Vaclav Kotesovec, Dec 03 2012

cp's OEIS Frontend

A052980 Expansion of (1 - x)/(1 - 2*x - x^3).

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Magma

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A219866 Number A(n,k) of tilings of a k X n rectangle using dominoes and straight (3 X 1) trominoes; square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A364457 Number A(n,k) of tilings of a k X n rectangle using dominoes and trominoes (of any shape); square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A165716 Number of tilings of a 3 X n rectangle using dominoes and right trominoes.

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A165791 Number of tilings of a 4 X n rectangle using dominoes and right trominoes.

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A219994 Number of tilings of an n X n square using dominoes and right trominoes.

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A353877 Triangle read by rows: T(n,k) = number of tilings of a n X k rectangle using right trominoes, dominoes and 1 X 1 tiles, n >= 0, k = 0..n.

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Maxima

A219988 Number of tilings of a 5 X n rectangle using dominoes and right trominoes.

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