A234833 - OEIS

%I #30 Feb 10 2024 03:43:33

%S 1,44,2800,181952,11835136,769854464,50077757440,3257475448832,

%T 211893401092096,13783315988086784,896581954180218880,

%U 58321176214542221312,3793696247386269024256,246773678989074187157504

%N Number of tilings of a box with sides 2 X 2 X 3n in R^3 by boxes of sides Tricube-V(3-dimensional dominoes).

%C a(n): Number of tilings of a box with sides 2 X 2 X 3n in R^3 by boxes of sides Tricube-V(3-dimensional dominoes).

%H S. Atacan and U. Koten, <a href="https://commons.wikimedia.org/wiki/File:Tricube-V.pdf">F(1,6,n)</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (68,-192).

%F a(n) = 68*a(n-1) - 192*a(n-2).

%F G.f.: (1-24*x)/(1-68*x+192*x^2). - _L. Edson Jeffery_, Dec 31 2013

%F a(n) = (2^(n-1)/C)*((-5+C)*(17-C)^n+(5+C)*(17+C)^n), where C = sqrt(241). - _L. Edson Jeffery_, Dec 31 2013

%e With the 16 tricube-V blocks in R^3 how many dfferent types of 2 X 2 X 12 sized volumetric regions can be attained?

%e For a(1)=44 and a(2)=2800, a(3)=68*a(2)-192*a(1)=68*2800-192*44=181952.

%K nonn,easy

%O 0,2

%A _Sila Atacan_, Dec 31 2013

%E a(5) and a(6) corrected and more terms added by _L. Edson Jeffery_, Dec 31 2013