cp's OEIS Frontend

A164754 Number of n X 2 1..4 arrays with all 1's connected, all 2's connected, all 3's connected, all 4's 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.

%I A164754 #35 Sep 01 2020 12:26:49
%S A164754 1,8,25,50,83,124,173,230,295,368,449,538,635,740,853,974,1103,1240,
%T A164754 1385,1538,1699,1868,2045,2230,2423,2624,2833,3050,3275,3508,3749,
%U A164754 3998,4255,4520,4793,5074,5363,5660,5965,6278,6599,6928,7265,7610,7963,8324,8693
%N A164754 Number of n X 2 1..4 arrays with all 1's connected, all 2's connected, all 3's connected, all 4's 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.
%H A164754 R. H. Hardin, <a href="/A164754/b164754.txt">Table of n, a(n) for n=2..100</a>
%F A164754 Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=6.
%F A164754 Empirical g.f.: x^2*(1 + 5*x + 4*x^2 - 2*x^3) / (1 - x)^3. - _Colin Barker_, Mar 25 2018
%F A164754 Empirical: a(n) = 4*(n-2)^2 + 5*(n-2) -1 for n>=3. - _Bill McEachen_, Aug 31 2020
%e A164754 Some solutions for n=9:
%e A164754 ...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2
%e A164754 ...1.4...1.3...1.4...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2
%e A164754 ...1.4...3.3...1.4...1.2...1.2...1.1...2.2...1.2...3.2...1.1...1.2...1.2...1.2
%e A164754 ...1.4...3.4...1.4...1.2...1.2...4.1...2.3...1.2...3.2...3.1...1.2...1.1...1.4
%e A164754 ...1.4...3.4...1.4...1.2...1.2...4.1...2.3...2.2...3.2...3.1...3.2...4.4...1.4
%e A164754 ...1.4...3.4...3.4...2.2...1.1...4.1...2.3...2.3...3.2...3.1...3.2...3.4...3.4
%e A164754 ...1.4...3.4...3.4...2.3...4.4...4.4...3.3...2.3...3.4...3.1...3.2...3.4...3.4
%e A164754 ...3.4...3.4...3.4...3.3...3.4...3.4...3.4...3.3...3.4...3.1...3.4...3.4...3.4
%e A164754 ...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4
%t A164754 Join[{1}, Table[n*(4*n - 3) - 2, {n, 2, 100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *)
%K A164754 nonn
%O A164754 2,2
%A A164754 _R. H. Hardin_, Aug 24 2009