A164755 - OEIS

%I #7 Oct 02 2025 23:42:46

%S 8,80,258,480,644,752,850,956,1070,1184,1298,1412,1526,1640,1754,1868,

%T 1982,2096,2210,2324,2438,2552,2666,2780,2894,3008,3122,3236,3350,

%U 3464,3578,3692,3806,3920,4034,4148,4262

%N Number of nX3 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.

%F Empirical: a(n)=2*a(n-1)-a(n-2) for n>=11

%e Some solutions for n=4

%e ...1.1.2...1.1.2...1.2.2...1.2.2...1.1.2...1.2.2...1.2.2...1.2.2...1.4.2

%e ...1.1.2...3.2.2...1.2.4...1.3.4...1.2.2...2.2.3...1.2.2...1.1.4...1.4.2

%e ...3.4.2...3.2.4...2.2.4...1.3.4...3.3.4...3.3.3...1.4.4...3.1.4...1.4.2

%e ...3.4.4...3.4.4...3.4.4...3.3.4...3.3.4...3.4.4...3.3.4...3.4.4...3.4.4

%e ------

%e ...1.2.2...1.1.2...1.2.2...1.2.2...1.1.2...1.1.2...1.1.2...1.2.2...1.1.2

%e ...3.3.2...3.1.2...1.1.2...1.1.2...1.4.2...1.2.2...3.1.2...1.1.2...2.2.2

%e ...3.4.2...3.2.2...3.1.2...3.1.2...1.4.2...1.2.4...3.2.2...3.1.4...2.4.4

%e ...3.4.4...3.3.4...3.3.4...3.1.4...3.4.4...3.4.4...3.4.4...3.1.4...3.3.4

%K nonn

%O 2,1

%A _R. H. Hardin_, Aug 24 2009