A050974 - OEIS

A050974

Number of binary arrangements on n X n array without three adjacent 1's in a row or column.

1, 2, 16, 265, 16561, 3157010, 1828904402, 3323590649777, 18691199385898465, 325778072452564800064, 17617718915229579206450786, 2954164381835835259001326344913, 1536134628973698280539373190731911729, 2477137610106747308204461168746042225266836, 12387488188151269567355592399321080831513078632498, 192102098800681202990688566451981906679020804069237862571, 9238409697848267958752630399467598421213391733838644131510525089

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OFFSET

0,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.

LINKS

Table of n, a(n) for n=0..16.

Steven R. Finch, Hard Square Entropy Constant [Broken link]

Steven R. Finch, Hard Square Entropy Constant [From the Wayback machine]

Eric Weisstein's World of Mathematics, 01-Matrix.

MATHEMATICA

t[m_] := t[m] = Map[ArrayReshape[#, {m, m}] &, Tuples[{0, 1}, m^2]]; a[m_] := a[m] = Count[Table[AnyTrue[Flatten[{Table[Equal[1, t[m][[n, a, b]], t[m][[n, a, b + 1]], t[m][[n, a, b + 2]]], {a, 1, m}, {b, 1, m - 2}], Table[Equal[1, t[m][[n, a, b]], t[m][[n, a + 1, b]], t[m][[n, a + 2, b]]], {a, 1, m - 2}, {b, 1, m}]}], TrueQ], {n, 1, 2^(m^2)}], False]; (* Robert P. P. McKone, Jan 04 2022 *)

CROSSREFS

Any connected three 1's gives A067968.

Cf. A006506. Diagonal of A202471.

Sequence in context: A372513 A283685 A197458 * A012188 A217816 A000182

Adjacent sequences: A050971 A050972 A050973 * A050975 A050976 A050977

KEYWORD

nonn,hard

AUTHOR

Eric W. Weisstein

EXTENSIONS

More terms from R. H. Hardin, Feb 02 2002

a(0)=1 prepended and a(13)-a(16) from Peter J. Taylor, Sep 26 2024

STATUS

approved