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A238009
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Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 3 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=floor(n/2), read by rows.
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23
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1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 1, 3, 8, 3, 1, 3, 12, 8, 1, 4, 18, 22, 6, 1, 4, 24, 40, 22, 1, 5, 32, 73, 66, 10, 1, 5, 40, 112, 146, 48, 1, 6, 50, 172, 292, 174, 20, 1, 6, 60, 240, 516, 448, 116, 1, 7, 72, 335, 860, 1020, 464, 36, 1, 7, 84, 440, 1340, 2016, 1360, 256
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OFFSET
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2,6
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LINKS
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EXAMPLE
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The first 19 rows of T(n,k) are:
n\k 0 1 2 3 4 5 6 7 8 9 10
2 1 1
3 1 1
4 1 2 2
5 1 2 4
6 1 3 8 3
7 1 3 12 8
8 1 4 18 22 6
9 1 4 24 40 22
10 1 5 32 73 66 10
11 1 5 40 112 146 48
12 1 6 50 172 292 174 20
13 1 6 60 240 516 448 116
14 1 7 72 335 860 1020 464 36
15 1 7 84 440 1340 2016 1360 256
16 1 8 98 578 2010 3716 3400 1168 72
17 1 8 112 728 2890 6336 7432 3840 584
18 1 9 128 917 4046 10326 14864 10600 2920 136
19 1 9 144 1120 5502 16016 27536 25344 10600 1280
20 1 10 162 1368 7336 24066 48188 54992 31800 7080 272
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PROG
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(C++) See Gribble link.
(PARI)
T(n, k)={(2^k*binomial(n-1*k, k) + ((k%2==0)+(n%2==0||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-1*k-(k%2)-(n%2))/2, k\2))/4}
for(n=2, 20, for(k=0, floor(n/2), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017
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CROSSREFS
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Cf. A034851, A226048, A102541, A226290, 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.
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KEYWORD
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tabf,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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