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 A350336 Number of n X n ternary matrices with no two adjacent 0's. 1
 1, 3, 56, 7504, 6832640, 42780151808, 1836366011301888, 540795841280638713856, 1092417949346109029345132544, 15137179876232766647722798101823488, 1438787206346713875314130065804001328234496, 938091111277955250977701268973340995182098116509696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A two-dimensional generalization of A028859. 2^(n^2) < a(n) < 3^(n^2). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..30 EXAMPLE a(1) is trivial because all 3 1 X 1 matrices have no 2 adjacent 0's, whereas for a(2) the 56 matrices are: { {{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{0, 1}, {1, 2}}, {{0, 1}, {2, 0}}, {{0, 1}, {2, 1}}, {{0, 1}, {2, 2}}, {{0, 2}, {1, 0}}, {{0, 2}, {1, 1}}, {{0, 2}, {1, 2}}, {{0, 2}, {2, 0}}, {{0, 2}, {2, 1}}, {{0, 2}, {2, 2}}, {{1, 0}, {0, 1}}, {{1, 0}, {0, 2}}, {{1, 0}, {1, 1}}, {{1, 0}, {1, 2}}, {{1, 0}, {2, 1}}, {{1, 0}, {2, 2}}, {{1, 1}, {0, 1}}, {{1, 1}, {0, 2}}, {{1, 1}, {1, 0}}, {{1, 1}, {1, 1}}, {{1, 1}, {1, 2}}, {{1, 1}, {2, 0}}, {{1, 1}, {2, 1}}, {{1, 1}, {2, 2}}, {{1, 2}, {0, 1}}, {{1, 2}, {0, 2}}, {{1, 2}, {1, 0}}, {{1, 2}, {1, 1}}, {{1, 2}, {1, 2}}, {{1, 2}, {2, 0}}, {{1, 2}, {2, 1}}, {{1, 2}, {2, 2}}, {{2, 0}, {0, 1}}, {{2, 0}, {0, 2}}, {{2, 0}, {1, 1}}, {{2, 0}, {1, 2}}, {{2, 0}, {2, 1}}, {{2, 0}, {2, 2}}, {{2, 1}, {0, 1}}, {{2, 1}, {0, 2}}, {{2, 1}, {1, 0}}, {{2, 1}, {1, 1}}, {{2, 1}, {1, 2}}, {{2, 1}, {2, 0}}, {{2, 1}, {2, 1}}, {{2, 1}, {2, 2}}, {{2, 2}, {0, 1}}, {{2, 2}, {0, 2}}, {{2, 2}, {1, 0}}, {{2, 2}, {1, 1}}, {{2, 2}, {1, 2}}, {{2, 2}, {2, 0}}, {{2, 2}, {2, 1}}, {{2, 2}, {2, 2}} } MATHEMATICA t[m_] := t[m] = Map[ArrayReshape[#, {m, m}] &, Tuples[{0, 1, 2}, m^2]]; a[m_] := a[m] = Count[Table[AnyTrue[Flatten[{Table[Equal[0, t[m][[n, a, b]], t[m][[n, a, b + 1]]], {a, 1, m}, {b, 1, m - 1}], Table[Equal[0, t[m][[n, a, b]], t[m][[n, a + 1, b]]], {a, 1, m - 1}, {b, 1, m}]}], TrueQ], {n, 1, 3^(m^2)}], False]; Table[a[n], {n, 1, 3}] CROSSREFS Cf. A006506 for binary version. Cf. A028859 for one-dimensional version. Sequence in context: A335804 A070731 A132489 * A344690 A203483 A051227 Adjacent sequences: A350333 A350334 A350335 * A350337 A350338 A350339 KEYWORD nonn,hard AUTHOR Robert P. P. McKone, Jan 03 2022 EXTENSIONS Terms a(5)-a(11) from Andrew Howroyd, Jan 04 2022 STATUS approved

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Last modified June 19 13:40 EDT 2024. Contains 373503 sequences. (Running on oeis4.)