A165394 - OEIS

%I #7 Mar 26 2018 09:54:13

%S 1,9,37,105,241,481,869,1457,2305,3481,5061,7129,9777,13105,17221,

%T 22241,28289,35497,44005,53961,65521,78849,94117,111505,131201,153401,

%U 178309,206137,237105,271441,309381,351169,397057,447305,502181,561961,626929

%N Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 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 3 neighbors with the same value.

%H R. H. Hardin, <a href="/A165394/b165394.txt">Table of n, a(n) for n=2..99</a>

%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>=7.

%F Conjectures from _Colin Barker_, Mar 26 2018: (Start)

%F G.f.: x^2*(1 + x)*(1 + 3*x - x^2 + x^3) / (1 - x)^5.

%F a(n) = (15 - 20*n + 11*n^2 - 4*n^3 + n^4) / 3.

%F (End)

%e Some solutions for n=6:

%e ...1.1.2.2.2.2.....1.3.3.3.2.2.....1.1.1.1.1.2.....1.1.3.2.2.2..

%e .....3.3.4.4.4.4.....3.3.3.2.4.4.....3.3.2.2.2.4.....3.3.2.2.2.4

%e ------

%e ...1.1.1.2.2.2.....1.1.1.3.3.2.....1.3.3.3.2.2.....1.1.1.2.2.2..

%e .....3.1.1.4.4.4.....3.3.3.3.2.4.....3.3.3.3.2.4.....3.1.2.2.2.4

%e ------

%e ...1.1.1.1.4.2.....1.1.2.2.2.2.....1.3.2.2.2.2.....1.3.2.2.2.2..

%e .....3.3.4.4.4.4.....3.2.2.4.4.4.....3.3.3.3.4.4.....3.3.3.2.2.4

%K nonn

%O 2,2

%A _R. H. Hardin_, Sep 17 2009