A183638 - OEIS

%I #12 May 25 2021 04:28:27

%S 5684,9256,17612,38056,90524,231736,629132,1793416,5328764,16413016,

%T 52195052,170891176,574845404,1983103096,7003319372,25265467336,

%U 92897360444,347253741976,1316323506092,5047850897896,19540336713884

%N Number of (n+1) X 6 0..3 arrays with every 2 X 2 subblock summing to 6.

%C Column 5 of A183642.

%H R. H. Hardin, <a href="/A183638/b183638.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).

%F Conjectures from _Colin Barker_, Mar 31 2018: (Start)

%F G.f.: 4*x*(1421 - 11896*x + 30998*x^2 - 24576*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).

%F a(n) = 2702 + 301*2^(2+n) + 62*3^(1+n) + 4^(1+n).

%F (End)

%e Some solutions for 3 X 6:

%e   2 0 1 2 3 0    2 1 2 3 1 1    1 1 1 1 1 1    2 3 3 3 1 0

%e   1 3 2 1 0 3    1 2 1 0 2 2    3 1 3 1 3 1    1 0 0 0 2 3

%e   1 1 0 3 2 1    2 1 2 3 1 1    0 2 0 2 0 2    2 3 3 3 1 0

%Y Cf. A183642.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011