login
Number of lower triangles of an n X n 0..3 array with new values introduced in row major order 0..3 and no two horizontal or vertical neighbors of any element equal.
1

%I #18 May 05 2018 13:18:04

%S 1,3,24,192,1152,5760,26880,118272,506880,2119680,8761344,35807232,

%T 145539072,588349440,2372075520,9538240512,38303170560,153613762560,

%U 615659864064,2465854390272,9873068654592,39518019256320,158149336104960

%N Number of lower triangles of an n X n 0..3 array with new values introduced in row major order 0..3 and no two horizontal or vertical neighbors of any element equal.

%C Column 3 of A194893.

%H R. H. Hardin, <a href="/A194888/b194888.txt">Table of n, a(n) for n = 1..24</a>

%F Empirical (for n>=3): 9*2^(2*n-2) - (1-(-1)^n)*21/8*2^(3*n/2+1/2) - (1+(-1)^n)*15/4*2^(3*n/2) + 6*2^n. - _Vaclav Kotesovec_, Nov 27 2012

%F Empirical g.f.: x*(1 - 3*x + 6*x^2 + 96*x^3 + 80*x^4 - 192*x^5) / ((1 - 2*x)*(1 - 4*x)*(1 - 8*x^2)). - _Colin Barker_, May 05 2018

%e Some solutions for 4 X 4:

%e 0 0 0 0 0 0 0 0

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

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

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

%Y Cf. A194893.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 04 2011