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
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
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