cp's OEIS Frontend

A050974 Number of binary arrangements on n X n array without three adjacent 1's in a row or column.

%I A050974 #31 Feb 16 2025 08:32:41
%S A050974 1,2,16,265,16561,3157010,1828904402,3323590649777,18691199385898465,
%T A050974 325778072452564800064,17617718915229579206450786,
%U A050974 2954164381835835259001326344913,1536134628973698280539373190731911729,2477137610106747308204461168746042225266836,12387488188151269567355592399321080831513078632498,192102098800681202990688566451981906679020804069237862571,9238409697848267958752630399467598421213391733838644131510525089
%N A050974 Number of binary arrangements on n X n array without three adjacent 1's in a row or column.
%D A050974 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.
%H A050974 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/square/square.html">Hard Square Entropy Constant</a> [Broken link]
%H A050974 Steven R. Finch, <a href="http://web.archive.org/web/20010605012506/http://www.mathsoft.com/asolve/constant/square/square.html">Hard Square Entropy Constant</a> [From the Wayback machine]
%H A050974 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/01-Matrix.html">01-Matrix.</a>
%t A050974 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 *)
%Y A050974 Any connected three 1's gives A067968.
%Y A050974 Cf. A006506. Diagonal of A202471.
%K A050974 nonn,hard
%O A050974 0,2
%A A050974 _Eric W. Weisstein_
%E A050974 More terms from _R. H. Hardin_, Feb 02 2002
%E A050974 a(0)=1 prepended and a(13)-a(16) from _Peter J. Taylor_, Sep 26 2024