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).

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).

Links

Table of n, a(n) for n=0..13.

S. Atacan and U. Koten, F(1,6,n)

Index entries for linear recurrences with constant coefficients, signature (68,-192).

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

Adjacent sequences: A234830 A234831 A234832 * A234834 A234835 A234836

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