OFFSET
0,2
COMMENTS
Cycle index = 1/4(s_1^(n^2)+ 2 s_4^floor(n^2/4)s_1^(n mod 2)+s_2^floor(n^2/2)s_1^(n mod 2)). - Geoffrey Critzer, Oct 28 2011
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
Peter Kagey, Illustration of a(3)=140
Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv:2311.13072 [math.CO], 2023.
FORMULA
a(n) = (m^(n^2) + 2*m^((n^2 + 3*(n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 2.
EXAMPLE
a(2)=6 from
00 10 11 10 11 11
00 00 00 01 10 11
MATHEMATICA
Table[(2^(n^2)+2*2^Floor[n^2/4]*2^Mod[n, 2]+2^Floor[n^2/2]*2^Mod[n, 2])/4, {n, 0, 10}] (* Geoffrey Critzer, Oct 28 2011 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Apr 14 2021
STATUS
approved