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 A068920 Table of t(r,s) read by antidiagonals: t(r,s) is the number of ways to tile an r X s room with 1 X 2 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 Rows 2-6 are given in A068921 - A068925. LINKS Table of n, a(n) for n=1..94. Dean Hickerson, Filling rectangular rooms with Tatami mats EXAMPLE Table begins: 0, 1, 0, 1, 0, 1, ... 1, 2, 3, 4, 6, 9, ... 0, 3, 0, 4, 0, 6, ... 1, 4, 4, 2, 3, 3, ... 0, 6, 0, 3, 0, 2, ... 1, 9, 6, 3, 2, 2, ... ... 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. Cf. A068921 (row 2), A068922 (row 3), A068923 (row 4), A068924 (row 5), A068925 (row 6). Sequence in context: A291556 A323073 A167279 * A363882 A099390 A297477 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 April 20 03:03 EDT 2024. Contains 371798 sequences. (Running on oeis4.)