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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. 6
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870 FORMULA 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. EXAMPLE 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 CROSSREFS Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A243866, A006918, A244307, A248011, A248016, A248059, A248060, A248017, A248027. Sequence in context: A062068 A130542 A128502 * A079159 A192298 A254967 Adjacent sequences:  A244303 A244304 A244305 * A244307 A244308 A244309 KEYWORD tabl,nonn AUTHOR Christopher Hunt Gribble, Jun 25 2014 EXTENSIONS Terms corrected and extended by Christopher Hunt Gribble, Apr 02 2015 STATUS approved

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Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)