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 A068920 Table of t(r,s) by diagonals, where t(r,s) is the number of ways to tile an r X s room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point. 13
 0, 1, 1, 0, 2, 0, 1, 3, 3, 1, 0, 4, 0, 4, 0, 1, 6, 4, 4, 6, 1, 0, 9, 0, 2, 0, 9, 0, 1, 13, 6, 3, 3, 6, 13, 1, 0, 19, 0, 3, 0, 3, 0, 19, 0, 1, 28, 10, 3, 2, 2, 3, 10, 28, 1, 0, 41, 0, 5, 0, 2, 0, 5, 0, 41, 0, 1, 60, 16, 5, 2, 2, 2, 2, 5, 16, 60, 1, 0, 88, 0, 6, 0, 1, 0, 1, 0, 6, 0, 88, 0, 1, 129, 26 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table begins: t(1,1); t(1,2) t(2,1); t(1,3) t(2,2) t(3,1); ... Rows 2-6 are given in A068921 - A068925. LINKS Dean Hickerson, Filling rectangular rooms with Tatami mats MATHEMATICA (* See link for Mathematica programs. *) c[r_, s_] := Which[s<0, 0, r==1, 1 - Mod[s, 2], r == 2, c1[2, s] + c2[2, s] + Boole[s == 0], OddQ[r], c[r, s] = c[r, s - r + 1] + c[r, s - r - 1] + Boole[s == 0], EvenQ[r], c[r, s] = c1[r, s] + c2[r, s] + Boole[s == 0]]; c1[r_, s_] := Which[s <= 0, 0, r == 2, c[2, s - 1], EvenQ[r], c2[r, s - 1] + Boole[s == 1]]; c2[r_, s_] := Which[s <= 0, 0, r == 2, c2[2, s] = c1[2, s - 2] + Boole[s == 2], EvenQ[r], c2[r, s] = c1[r, s - r + 2] + c1[r, s - r] + Boole[s == r - 2] + Boole[s == r]]; t[r_, s_] := Which[r>s, t[s, r], OddQ[r] && r>1, 2 c[r, s], True, c[r, s]]; A068920[n_] := Module[{x}, x = Floor[(Sqrt[8 n + 1] - 1)/2]; t[n + 1 - x (x + 1)/2, (x + 1) (x + 2)/2 - n]]; Table[A068920[n], {n, 0, 100}] (* Jean-François Alcover, May 12 2017, copied and adapted from Dean Hickerson's programs *) CROSSREFS Cf. A068926 for incongruent tilings, A067925 for count by area, A068921 for row 2, A068922 for row 3, A068923 for row 4, A068924 for row 5, A068925 for row 6. Sequence in context: A291556 A323073 A167279 * A099390 A297477 A124031 Adjacent sequences:  A068917 A068918 A068919 * A068921 A068922 A068923 KEYWORD nonn,tabl AUTHOR Dean Hickerson, Mar 11 2002 STATUS approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)