A225812 -id:A225812 - cp's OEIS frontend

A238583 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

1, 3, 2, 1, 3, 4, 1, 6, 9, 1, 6, 14, 1, 9, 32, 18, 4, 1, 9, 55, 65, 23, 1, 12, 91, 164, 87, 1, 12, 132, 320, 229, 1, 15, 186, 608, 648, 134, 10, 1, 15, 245, 1043, 1633, 770, 106, 1, 18, 317, 1736, 3659, 2800, 646, 1, 18, 394, 2666, 7247, 7572, 2510

Offset: 4

Christopher Hunt Gribble, Mar 01 2014

			The first 8 rows of T(n,k) are:
.\ k    0      1      2      3      4
n
4       1      3      2
5       1      3      4
6       1      6      9
7       1      6     14
8       1      9     32     18      4
9       1      9     55     65     23
10      1     12     91    164     87
11      1     12    132    320    229

Andrew Howroyd, Table of n, a(n) for n = 4..992
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581, A238582, A228169, A238586, A238592

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(26) and beyond from Andrew Howroyd, May 29 2017

A238586 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=5*floor(n/2), read by rows.

Original entry on oeis.org

1, 5, 16, 19, 9, 1, 1, 5, 32, 73, 66, 10, 1, 10, 85, 377, 961, 1348, 1080, 472, 111, 12, 1, 1, 10, 142, 1011, 4429, 11370, 17252, 14478, 6094, 1020, 70, 1, 15, 236, 2280, 14203, 56571, 146212, 244063, 261847, 179063, 77974, 21422, 3637, 368, 24, 1

Offset: 2

Christopher Hunt Gribble, Mar 01 2014

			The first 4 rows of T(n,k) are:
.\k  0     1     2     3     4     5     6     7     8     9    10
n
2    1     5    16    19     9     1
3    1     5    32    73    66    10
4    1    10    85   377   961  1348  1080   472   111    12     1
5    1    10   142  1011  4429 11370 17252 14478  6094  1020    70

Andrew Howroyd, Table of n, a(n) for n = 2..937
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238592.

Terms corrected and crossrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(36) and beyond from Andrew Howroyd, May 29 2017

A238592 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=3*floor(n/3), read by rows.

Original entry on oeis.org

1, 4, 9, 2, 1, 4, 18, 8, 1, 8, 42, 28, 1, 8, 77, 165, 151, 44, 6, 1, 12, 133, 521, 891, 543, 106, 1, 12, 200, 1160, 3022, 2756, 824, 1, 16, 288, 2260, 8443, 13336, 9364, 2819, 387, 20, 1, 16, 387, 3867, 19833, 48418, 58731, 34797, 9462, 900

Offset: 3

Christopher Hunt Gribble, Mar 01 2014

			The first 6 rows of T(n,k) are:
.\ k    0      1      2      3      4      5      6
n
3       1      4      9      2
4       1      4     18      8
5       1      8     42     28
6       1      8     77    165    151     44      6
7       1     12    133    521    891    543    106
8       1     12    200   1160   3022   2756    824

Andrew Howroyd, Table of n, a(n) for n = 3..989
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586.

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(36) and beyond from Andrew Howroyd, May 29 2017

A238558 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

Original entry on oeis.org

1, 3, 4, 1, 3, 8, 1, 6, 18, 1, 6, 36, 32, 13, 1, 9, 64, 128, 87, 1, 9, 100, 308, 332, 1, 12, 146, 647, 1118, 451, 68, 1, 12, 200, 1160, 3022, 2756, 824, 1, 15, 264, 1958, 6882, 10076, 5009, 1, 15, 336, 3020, 13798, 28774, 24237, 4774, 346

Offset: 3

Christopher Hunt Gribble, Feb 28 2014

			The first 8 rows of T(n,k) are:
.\ k    0      1      2      3      4      5      6
n
3       1      3      4
4       1      3      8
5       1      6     18
6       1      6     36     32     13
7       1      9     64    128     87
8       1      9    100    308    332
9       1     12    146    647   1118    451     68
10      1     12    200   1160   3022   2756    824

Andrew Howroyd, Table of n, a(n) for n = 3..971
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557, A238559, A228168, A238581-A238583, A228169, A238586, A238592.

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(41) and beyond from Andrew Howroyd, May 29 2017

A238582 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

Original entry on oeis.org

1, 4, 6, 1, 1, 4, 12, 3, 1, 8, 28, 10, 1, 8, 54, 82, 49, 8, 1, 1, 12, 95, 283, 311, 91, 10, 1, 12, 146, 647, 1118, 451, 68, 1, 16, 212, 1300, 3380, 3076, 1200, 209, 20, 1, 1, 16, 288, 2260, 8443, 13336, 9364, 2819, 387, 20

Offset: 3

Christopher Hunt Gribble, Mar 01 2014

			The first 9 rows of T(n,k) are:
.\ k  0     1     2     3     4     5     6     7     8     9
n
3     1     4     6     1
4     1     4    12     3
5     1     8    28    10
6     1     8    54    82    49     8     1
7     1    12    95   283   311    91    10
8     1    12   146   647  1118   451    68
9     1    16   212  1300  3380  3076  1200   209    20     1
10    1    16   288  2260  8443 13336  9364  2819   387    20
11    1    20   379  3709 18203 42412 44599 19051  3682   282

Andrew Howroyd, Table of n, a(n) for n = 3..989
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581, A238583, A228169, A238586, A238592.

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(46) and beyond from Andrew Howroyd, May 29 2017

A238551 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

Original entry on oeis.org

1, 2, 1, 1, 2, 2, 1, 4, 4, 1, 4, 11, 3, 1, 1, 6, 21, 13, 4, 1, 6, 36, 32, 13, 1, 8, 54, 82, 49, 8, 1, 1, 8, 77, 165, 151, 44, 6, 1, 10, 103, 319, 382, 173, 31, 1, 10, 134, 530, 867, 559, 164, 12, 1, 1, 12, 168, 852, 1789, 1632, 705, 119, 9

Offset: 3

Christopher Hunt Gribble, Feb 28 2014

			The first 12 rows of T(n,k) are:
.\ k  0     1     2     3     4     5     6     7     8
n
3     1     2     1
4     1     2     2
5     1     4     4
6     1     4    11     3     1
7     1     6    21    13     4
8     1     6    36    32    13
9     1     8    54    82    49     8     1
10    1     8    77   165   151    44     6
11    1    10   103   319   382   173    31
12    1    10   134   530   867   559   164    12     1
13    1    12   168   852  1789  1632   705   119     9
14    1    12   207  1255  3409  4074  2406   618    66

Andrew Howroyd, Table of n, a(n) for n = 3..971
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015

Terms a(57) and beyond from Andrew Howroyd, May 29 2017

A243866 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing one 1 X 1 tile in an n X k rectangle under all symmetry operations of the rectangle.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 4, 2, 3, 3, 3, 4, 4, 3, 3, 4, 3, 6, 4, 6, 3, 4, 4, 4, 6, 6, 6, 6, 4, 4, 5, 4, 8, 6, 9, 6, 8, 4, 5, 5, 5, 8, 8, 9, 9, 8, 8, 5, 5, 6, 5, 10, 8, 12, 9, 12, 8, 10, 5, 6, 6, 6, 10, 10, 12, 12, 12, 12, 10, 10, 6, 6, 7, 6, 12, 10, 15

Offset: 1

Christopher Hunt Gribble, Jun 19 2014

It appears that the number of equivalence classes of ways of placing one m X m tile in an n X k rectangle under all symmetry operations of the rectangle is T(n-m+1,k-m+1) for m >= 2, n >= m and k >= m, and zero otherwise. - Christopher Hunt Gribble, Oct 17 2014
The sum over each antidiagonal of A243866
= Sum_{j=1..n}(2*j + 1 - (-1)^j)*(2*(n - j + 1) + 1 - (-1)^(n - j + 1))/16
= (n + 2)*(2*n^2 + 8*n + 3 - 3*(-1)^n)/48
- see A006918. - Christopher Hunt Gribble, Apr 01 2015

			T(n,k) for 1<=n<=11 and 1<=k<=11 is:
    k    1    2    3    4    5    6    7    8    9   10   11 ...
.n
.1       1    1    2    2    3    3    4    4    5    5    6
.2       1    1    2    2    3    3    4    4    5    5    6
.3       2    2    4    4    6    6    8    8   10   10   12
.4       2    2    4    4    6    6    8    8   10   10   12
.5       3    3    6    6    9    9   12   12   15   15   18
.6       3    3    6    6    9    9   12   12   15   15   18
.7       4    4    8    8   12   12   16   16   20   20   24
.8       4    4    8    8   12   12   16   16   20   20   24
.9       5    5   10   10   15   15   20   20   25   25   30
10       5    5   10   10   15   15   20   20   25   25   30
11       6    6   12   12   18   18   24   24   30   30   36
...

Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870

Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A006918, A244306, A244307, A248011, A248016, A248059, A248060, A248017, A248027.

b := proc (n,k);
floor((1/2)*n+1/2)*floor((1/2)*k+1/2)
end proc;
seq(seq(b(n, k-n+1), n = 1 .. k), k = 1 .. 140);

Empirically,
T(n,k) = floor((n+1)/2)*floor((k+1)/2)
       = (2*n+1-(-1)^n)*(2*k+1-(-1)^k)/4;
T(n,1) = A034851(n,1);
T(n,2) = A226048(n,1);
T(n,3) = A226290(n,1);
T(n,4) = A225812(n,1);
T(n,5) = A228022(n,1);
T(n,6) = A228165(n,1);
T(n,7) = A228166(n,1). - Christopher Hunt Gribble, May 01 2015

Terms corrected by Christopher Hunt Gribble, Mar 27 2015

A244306 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing two 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle.

Original entry on oeis.org

0, 1, 1, 2, 3, 2, 4, 6, 6, 4, 6, 10, 13, 10, 6, 9, 15, 22, 22, 15, 9, 12, 21, 34, 36, 34, 21, 12, 16, 28, 48, 56, 56, 48, 28, 16, 20, 36, 65, 78, 88, 78, 65, 36, 20, 25, 45, 84, 106, 123, 123, 106, 84, 45, 25, 30, 55, 106, 136, 168, 171, 168, 136, 106, 55, 30

Offset: 1

Christopher Hunt Gribble, Jun 25 2014

			T(n,k) for 1<=n<=11 and 1<=k<=11 is:
    k  1    2    3    4    5    6    7    8    9   10   11 ...
.n
.1     0    1    2    4    6    9   12   16   20   25   30
.2     1    3    6   10   15   21   28   36   45   55   66
.3     2    6   13   22   34   48   65   84  106  130  157
.4     4   10   22   36   56   78  106  136  172  210  254
.5     6   15   34   56   88  123  168  216  274  335  406
.6     9   21   48   78  123  171  234  300  381  465  564
.7    12   28   65  106  168  234  321  412  524  640  777
.8    16   36   84  136  216  300  412  528  672  820  996
.9    20   45  106  172  274  381  524  672  856 1045 1270
10    25   55  130  210  335  465  640  820 1045 1275 1550
11    30   66  157  254  406  564  777  996 1270 1550 1885

Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870

Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A243866, A006918, A244307, A248011, A248016, A248059, A248060, A248017, A248027.

Empirically,
T(n,k) = (4*k^2*n^2 + 2*k^2 + 8*k*n + 2*n^2 - 4*k - 4*n - 1 - (2*k^2 - 4*k - 1)*(-1)^n - (2*n^2 - 4*n - 1)*(-1)^k - (-1)^k*(-1)^n)/32.
T(1,k) = A002620(k) = floor(k^2/4).
T(2,k) = A000217(k) = k*(k+1)/2.
       = T(1,k) + T(1,k+1) = floor(k^2/4) + floor((k+1)^2/4).
T(3,k) = 2*A000217(k) + A024206(k-2)
       = k*(k+1) + floor((k-1)^2/4) - 1.

Terms corrected and extended by Christopher Hunt Gribble, Apr 02 2015

A248011 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing three 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 6, 6, 2, 6, 14, 27, 14, 6, 10, 32, 60, 60, 32, 10, 19, 55, 129, 140, 129, 55, 19, 28, 94, 218, 294, 294, 218, 94, 28, 44, 140, 363, 506, 608, 506, 363, 140, 44, 60, 208, 536, 832, 1038, 1038, 832, 536, 208, 60, 85, 285, 785, 1240, 1695

Offset: 1

Christopher Hunt Gribble, Sep 29 2014

			T(n,k) for 1<=n<=9 and 1<=k<=9 is:
   k    1     2     3     4     5     6     7     8     9 ...
n
1       0     0     1     2     6    10    19    28    44
2       0     1     6    14    32    55    94   140   208
3       1     6    27    60   129   218   363   536   785
4       2    14    60   140   294   506   832  1240  1802
5       6    32   129   294   608  1038  1695  2516  3642
6      10    55   218   506  1038  1785  2902  4324  6242
7      19    94   363   832  1695  2902  4703  6992 10075
8      28   140   536  1240  2516  4324  6992 10416 14988
9      44   208   785  1802  3642  6242 10075 14988 21544

Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870

Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A243866, A006918, A244306, A244307, A248016, A248059, A248060, A248017, A248027.

b := proc (n::integer, k::integer)::integer;
(4*k^3*n^3 - 12*k^2*n^2 + 2*k^3 + 6*k^2*n + 6*k*n^2 + 2*n^3 - 12*k^2 + 11*k*n - 12*n^2 + 4*k + 4*n - 3 - (2*k^3 + 6*k^2*n - 12*k^2 + 3*k*n + 4*k - 3)*(-1)^n - (6*k*n^2 + 2*n^3 + 3*k*n - 12*n^2 + 4*n - 3)*(-1)^k + (3*k*n - 3)*(-1)^k*(-1)^n)*(1/96);
end proc;
f := seq(seq(b(n, k - n + 1), n = 1 .. k), k = 1 .. 140);

Empirically,
T(n,k) = (4*k^3*n^3 - 12*k^2*n^2 + 2*k^3 + 6*k^2*n + 6*k*n^2 + 2*n^3 - 12*k^2 + 11*k*n - 12*n^2 + 4*k + 4*n - 3 - (2*k^3 + 6*k^2*n - 12*k^2 + 3*k*n + 4*k - 3)*(-1)^n - (6*k*n^2 + 2*n^3 + 3*k*n - 12*n^2 + 4*n - 3)*(-1)^k + (3*k*n - 3)*(-1)^k*(-1)^n)/96;
T(1,k) = A005993(k-3) = (k-1)*(2*(k-2)*k + 3*(1-(-1)^k))/24;
T(2,k) = A225972(k) = (k-1)*(2*k*(2*k-1) + 3*(1-(-1)^k))/12;
T(2,k) - T(1,k) = A199771(k-1) and A212561(k) = (k-1)*(6*k^2 + 3*(1-(-1)^k))/24.

Terms corrected and extended by Christopher Hunt Gribble, Apr 01 2015

A248017 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing five 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 14, 39, 14, 1, 3, 66, 208, 208, 66, 3, 12, 198, 794, 1092, 794, 198, 12, 28, 508, 2196, 3912, 3912, 2196, 508, 28, 66, 1092, 5231, 10626, 13462, 10626, 5231, 1092, 66, 126, 2156, 10808, 24648, 35787, 35787, 24648, 10808, 2156, 126

Offset: 1

Christopher Hunt Gribble, Sep 30 2014

			T(n,k) for 1<=n<=8 and 1<=k<=8 is:
.  k   1      2      3      4      5      6      7       8 ...
n
1      0      0      0      0      1      3     12      28
2      0      0      2     14     66    198    508    1092
3      0      2     39    208    794   2196   5231   10808
4      0     14    208   1092   3912  10626  24648   50344
5      1     66    794   3912  13462  35787  81648  164980
6      3    198   2196  10626  35787  94248 212988  428076
7     12    508   5231  24648  81648 212988 477903  955856
8     28   1092  10808  50344 164980 428076 955856 1906128

Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870

Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A243866, A006918, A244306, A244307, A248011, A248016, A248059, A248060, A248027.

b := proc (n::integer, k::integer)::integer;
(4*k^5*n^5 - 40*k^4*n^4 + 140*k^3*n^3 + 2*k^5 + 20*k^4*n
   + 30*k^3*n^2 + 30*k^2*n^3 + 20*k*n^4 + 2*n^5 - 40*k^4
   - 120*k^3*n - 185*k^2*n^2 - 120*k*n^3 - 40*n^4 + 160*k^3
   - 20*k^2*n - 20*k*n^2 + 160*n^3 - 80*k^2 + 36*k*n - 80*n^2
   + 48*k + 48*n + 45
   + (- 30*k^2*n^3 - 20*k*n^4 - 2*n^5 - 15*k^2*n^2 + 120*k*n^3
      + 40*n^4 + 20*k*n^2 - 160*n^3 + 60*k*n + 80*n^2 - 48*n
      - 45)*(-1)^k
   + (- 2*k^5 - 20*k^4*n - 30*k^3*n^2 + 40*k^4 + 120*k^3*n
      - 15*k^2*n^2 - 160*k^3 + 20*k^2*n + 80*k^2 + 60*k*n
      - 48*k - 45)*(-1)^n
   + (15*k^2*n^2 - 60*k*n + 45)*(-1)^k*(-1)^n)/1920;
end proc;
seq(seq(b(n, k-n+1), n = 1 .. k), k = 1 .. 140);

Empirically,
T(n,k) = (4*k^5*n^5 - 40*k^4*n^4 + 140*k^3*n^3 + 2*k^5 + 20*k^4*n + 30*k^3*n^2 + 30*k^2*n^3 + 20*k*n^4 + 2*n^5 - 40*k^4 - 120*k^3*n - 185*k^2*n^2 - 120*k*n^3 - 40*n^4 + 160*k^3 - 20*k^2*n - 20*k*n^2 + 160*n^3 - 80*k^2 + 36*k*n - 80*n^2 + 48*k + 48*n + 45
+ (- 30*k^2*n^3 - 20*k*n^4 - 2*n^5 - 15*k^2*n^2 + 120*k*n^3 + 40*n^4 + 20*k*n^2 - 160*n^3 + 60*k*n + 80*n^2 - 48*n - 45)*(-1)^k
+ (- 2*k^5 - 20*k^4*n - 30*k^3*n^2 + 40*k^4 + 120*k^3*n - 15*k^2*n^2 - 160*k^3 + 20*k^2*n + 80*k^2 + 60*k*n - 48*k - 45)*(-1)^n
+ (15*k^2*n^2 - 60*k*n + 45)*(-1)^k*(-1)^n)/1920;
T(1,k) = A005995(k-5) = (k-3)*(k-1)*((k-4)*(k-2)*2*k + 15*(1-(-1)^k))/480;
T(2,k) = A222715(k) = (k-2)*(k-1)*((2*k-3)(2*k-1)*2*k + 15*(1-(-1)^k))/120.

Terms corrected and extended by Christopher Hunt Gribble, Apr 16 2015

cp's OEIS Frontend

A238583 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

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A238586 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=5*floor(n/2), read by rows.

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A238592 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 10 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=3*floor(n/3), read by rows.

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A238558 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

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A238582 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

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A238551 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 6 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.

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A243866 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing one 1 X 1 tile in an n X k rectangle under all symmetry operations of the rectangle.

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A244306 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing two 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle.

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A248011 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing three 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle.

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