A164749 - OEIS

A164749

Number of n X 3 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, and 4 in the lower right corner.

%I #10 Mar 26 2018 09:54:46

%S 8,108,730,3576,14414,50928,163722,490496,1391862,3784168,9940066,

%T 25384568,63327166,154906432,372640634,883653200,2069574918,

%U 4794856504,11003621330,25040248584,56557140046,126889144656,282971569898

%N Number of n X 3 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, and 4 in the lower right corner.

%H R. H. Hardin, <a href="/A164749/b164749.txt">Table of n, a(n) for n = 2..52</a>

%F Empirical: a(n) = 12*a(n-1) - 63*a(n-2) + 190*a(n-3) - 363*a(n-4) + 456*a(n-5) - 377*a(n-6) + 198*a(n-7) - 60*a(n-8) + 8*a(n-9) for n >= 11.

%F Empirical g.f.: 2*x^2*(4 + 6*x - 31*x^2 + 50*x^3 - 62*x^4 + 52*x^5 - 7*x^6 - 12*x^7 + 4*x^8) / ((1 - x)^6*(1 - 2*x)^3). - _Colin Barker_, Mar 25 2018

%e Some solutions for n=4:

%e 1 1 2 1 2 2 1 1 2 1 1 2 1 2 2 1 1 2 1 1 2 1 1 2 1 2 2

%e 1 1 1 1 4 4 1 4 4 3 2 2 2 2 2 3 3 2 3 1 2 1 1 1 1 1 4

%e 3 4 4 4 4 4 4 4 4 3 2 4 4 4 2 3 3 2 3 3 4 3 1 1 1 1 4

%e 3 3 4 3 3 4 3 3 4 3 4 4 3 4 4 3 4 4 3 3 4 3 4 4 3 4 4

%e ------

%e 1 2 2 1 1 2 1 4 2 1 2 2 1 2 2 1 2 2 1 2 2 1 1 2 1 2 2

%e 1 2 2 1 2 2 1 4 4 1 3 2 1 1 1 3 3 3 1 2 2 3 4 2 1 1 2

%e 2 2 4 1 2 2 1 4 4 3 3 3 3 3 3 3 3 4 3 3 2 3 4 4 3 1 4

%e 3 3 4 3 4 4 3 3 4 3 4 4 3 3 4 3 4 4 3 3 4 3 3 4 3 1 4

%K nonn

%O 2,1

%A _R. H. Hardin_, Aug 24 2009