A238552 -id:A238552 - cp's OEIS frontend

A238557 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

1, 4, 9, 6, 1, 1, 4, 18, 22, 6, 1, 8, 49, 139, 204, 145, 54, 8, 1, 1, 8, 83, 392, 1056, 1438, 956, 240, 25, 1, 12, 139, 927, 3731, 8772, 12069, 9506, 4366, 1160, 179, 16, 1, 1, 12, 198, 1742, 9748, 33644, 73274, 98779, 80661, 37886, 9679, 1258, 72

Offset: 2

Christopher Hunt Gribble, Feb 28 2014

			The first 4 rows of T(n,k) are:
.\ k  0     1     2     3     4     5     6     7     8
n
2     1     4     9     6     1
3     1     4    18    22     6
4     1     8    49   139   204   145    54     8     1
5     1     8    83   392  1056  1438   956   240    25

Andrew Howroyd, Table of n, a(n) for n = 2..991
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, A238558, A238559, A228168, A238581-A238583, A228169, A238586, A238592.

tabf,nonn

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

A238559 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

Original entry on oeis.org

1, 3, 1, 1, 3, 2, 1, 6, 4, 1, 6, 6, 1, 9, 17, 5, 1, 1, 9, 32, 18, 4, 1, 12, 56, 46, 13, 1, 12, 84, 90, 31, 1, 15, 121, 193, 98, 13, 1, 1, 15, 162, 360, 275, 66, 6, 1, 18, 212, 664, 672, 250, 31, 1, 18, 266, 1080, 1408, 672, 110, 1, 21, 329, 1711, 2797, 1772, 432, 23, 1

Offset: 4

Christopher Hunt Gribble, Feb 28 2014

			The first 11 rows of T(n,k) are:
.\  k   0      1      2      3      4     5     6
n
4       1      3      1
5       1      3      2
6       1      6      4
7       1      6      6
8       1      9     17      5      1
9       1      9     32     18      4
10      1     12     56     46     13
11      1     12     84     90     31
12      1     15    121    193     98    13     1
13      1     15    162    360    275    66     6
14      1     18    212    664    672   250    31

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, A238558, A228168, A238581-A238583, A228169, A238586, A238592.

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

Terms a(31) and beyond from Andrew Howroyd, May 29 2017

A238581 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

Original entry on oeis.org

1, 4, 12, 10, 3, 1, 4, 24, 40, 22, 1, 8, 65, 230, 467, 476, 269, 70, 9, 1, 8, 109, 641, 2281, 4424, 4718, 2409, 473, 1, 12, 182, 1479, 7644, 24024, 47022, 56226, 41000, 17834, 4545, 625, 39, 1, 12, 258, 2762, 19347, 86536, 255552, 495547, 625705, 499314, 239254, 61732, 6533

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
n
2     1     4    12    10     3
3     1     4    24    40    22
4     1     8    65   230   467   476   269    70     9
5     1     8   109   641  2281  4424  4718  2409   473

Andrew Howroyd, Table of n, a(n) for n = 2..991
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, A238582, A238583, A228169, A238586, A238592.

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

Terms a(43) and beyond from Andrew Howroyd, May 29 2017

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.

Original entry on oeis.org

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

A257523 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

Original entry on oeis.org

1, 2, 1, 2, 1, 4, 1, 4, 1, 6, 6, 1, 6, 14, 1, 8, 28, 1, 8, 44, 1, 10, 66, 20, 1, 10, 90, 64, 1, 12, 120, 168, 1, 12, 152, 320, 1, 14, 190, 572, 72, 1, 14, 230, 896, 328, 1, 16, 276, 1360, 984, 1, 16, 324, 1920, 2264, 1, 18, 378, 2660, 4528, 272

Offset: 4

Christopher Hunt Gribble, Apr 27 2015

			The first 9 rows of T(n,k) are:
.\ k    0      1      2     3
n
4       1      2
5       1      2
6       1      4
7       1      4
8       1      6      6
9       1      6     14
10      1      8     28
11      1      8     44
12      1     10     66    20
13      1     10     90    64
14      1     12    120   168
15      1     12    152   320

Andrew Howroyd, Table of n, a(n) for n = 4..860
Christopher Hunt Gribble, C++ program

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592

T(n,k)={(4^k*binomial(n-3*k,k) + ((n%2==0||k%2==0)+(k%2==0)+(k==0)) * 4^((k+1)\2)*binomial((n-3*k-(k%2)-(n%2))/2,k\2))/4}
for(n=4,15,for(k=0,(n\4), print1(T(n,k), ", "));print) \\ Andrew Howroyd, May 29 2017

Terms a(24) and beyond by Andrew Howroyd, May 29 2017

cp's OEIS Frontend

A238557 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

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A238559 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 8 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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A238581 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

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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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A257523 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows.

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