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 A189006 Array A(m,n) read by antidiagonals: number of domino tilings of the m X n grid with upper left corner removed iff m*n is odd, (m>=0, n>=0). 8
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 5, 4, 5, 1, 1, 1, 1, 8, 11, 11, 8, 1, 1, 1, 1, 13, 15, 36, 15, 13, 1, 1, 1, 1, 21, 41, 95, 95, 41, 21, 1, 1, 1, 1, 34, 56, 281, 192, 281, 56, 34, 1, 1, 1, 1, 55, 153, 781, 1183, 1183, 781, 153, 55, 1, 1, 1, 1, 89, 209, 2245, 2415, 6728, 2415, 2245, 209, 89, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Alois P. Heinz, Antidiagonals n = 0..75, flattened Eric Weisstein's World of Mathematics, Perfect Matching Wikipedia, FKT algorithm Wikipedia, Matching (graph theory) EXAMPLE A(3,3) = 4, because there are 4 domino tilings of the 3 X 3 grid with upper left corner removed:   . .___. . .___. . .___. . .___.   ._|___| ._|___| ._| | | ._|___|   | |___| | | | | | |_|_| |___| |   |_|___| |_|_|_| |_|___| |___|_| Array begins:   1, 1,  1,  1,   1,    1,    1, ...   1, 1,  1,  1,   1,    1,    1, ...   1, 1,  2,  3,   5,    8,   13, ...   1, 1,  3,  4,  11,   15,   41, ...   1, 1,  5, 11,  36,   95,  281, ...   1, 1,  8, 15,  95,  192, 1183, ...   1, 1, 13, 41, 281, 1183, 6728, ... MAPLE with(LinearAlgebra): A:= proc(m, n) option remember; local i, j, s, t, M;       if m=0 or n=0 then 1     elif m1 or j>1 or s=0 then                if j 1 || j > 1 || s == 0, If[j < m, M[t, t+1] = 1]; If[i < n, M[t, t+m] = 1-2*Mod[j, 2]]]]]; Sqrt[Det[Array[M, {n*m-s, n*m-s}]]]]]; Table[Table[A[m, d-m], {m, 0, d}], {d, 0, 15}] // Flatten (* Jean-François Alcover, Dec 26 2013, translated from Maple *) CROSSREFS Rows m=0+1, 2-12 give: A000012, A000045(n+1), A002530(n+1), A005178(n+1), A189003, A028468, A189004, A028470, A189005, A028472, A210724, A028474. Main diagonal gives: A189002. Cf. A099390, A187596, A187616, A187617, A187618, A004003. Sequence in context: A193517 A296554 A327482 * A245013 A219924 A226444 Adjacent sequences:  A189003 A189004 A189005 * A189007 A189008 A189009 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Apr 15 2011 STATUS approved

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Last modified October 18 05:45 EDT 2019. Contains 328146 sequences. (Running on oeis4.)