cp's OEIS Frontend

A238009 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.

%I A238009 #38 May 30 2017 12:14:22
%S A238009 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,
%T A238009 73,66,10,1,5,40,112,146,48,1,6,50,172,292,174,20,1,6,60,240,516,448,
%U A238009 116,1,7,72,335,860,1020,464,36,1,7,84,440,1340,2016,1360,256
%N A238009 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.
%H A238009 Christopher Hunt Gribble and Andrew Howroyd, <a href="/A238009/b238009.txt">Rows n=2..60 of T(n,k) flattened</a> (Rows n=2..20 from Christopher Hunt Gribble)
%H A238009 Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e A238009 The first 19 rows of T(n,k) are:
%e A238009    n\k 0  1   2    3    4     5     6     7     8    9  10
%e A238009    2   1  1
%e A238009    3   1  1
%e A238009    4   1  2   2
%e A238009    5   1  2   4
%e A238009    6   1  3   8    3
%e A238009    7   1  3  12    8
%e A238009    8   1  4  18   22    6
%e A238009    9   1  4  24   40   22
%e A238009   10   1  5  32   73   66    10
%e A238009   11   1  5  40  112  146    48
%e A238009   12   1  6  50  172  292   174    20
%e A238009   13   1  6  60  240  516   448   116
%e A238009   14   1  7  72  335  860  1020   464    36
%e A238009   15   1  7  84  440 1340  2016  1360   256
%e A238009   16   1  8  98  578 2010  3716  3400  1168    72
%e A238009   17   1  8 112  728 2890  6336  7432  3840   584
%e A238009   18   1  9 128  917 4046 10326 14864 10600  2920  136
%e A238009   19   1  9 144 1120 5502 16016 27536 25344 10600 1280
%e A238009   20   1 10 162 1368 7336 24066 48188 54992 31800 7080 272
%o A238009 (C++) See Gribble link.
%o A238009 (PARI)
%o A238009 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}
%o A238009 for(n=2,20,for(k=0,floor(n/2), print1(T(n,k), ", "));print) \\ _Andrew Howroyd_, May 29 2017
%Y A238009 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.
%K A238009 tabf,nonn
%O A238009 2,6
%A A238009 _Christopher Hunt Gribble_, Feb 16 2014
%E A238009 Corrected C++ program and xrefs added by _Christopher Hunt Gribble_, Apr 25 2015