login
A234833
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).
0
1, 44, 2800, 181952, 11835136, 769854464, 50077757440, 3257475448832, 211893401092096, 13783315988086784, 896581954180218880, 58321176214542221312, 3793696247386269024256, 246773678989074187157504
OFFSET
0,2
COMMENTS
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).
FORMULA
a(n) = 68*a(n-1) - 192*a(n-2).
G.f.: (1-24*x)/(1-68*x+192*x^2). - L. Edson Jeffery, Dec 31 2013
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
EXAMPLE
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?
For a(1)=44 and a(2)=2800, a(3)=68*a(2)-192*a(1)=68*2800-192*44=181952.
CROSSREFS
Sequence in context: A329302 A359885 A271137 * A282186 A200899 A220599
KEYWORD
nonn,easy
AUTHOR
Sila Atacan, Dec 31 2013
EXTENSIONS
a(5) and a(6) corrected and more terms added by L. Edson Jeffery, Dec 31 2013
STATUS
approved