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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
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
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.)