OFFSET
0,8
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..860
Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv:2311.13072 [math.CO], 2023. See p. 3.
FORMULA
T(n,k) = (k^(n^2) + 2*k^((n^2 + 3*(n mod 2))/4) + k^((n^2 + (n mod 2))/2))/4.
EXAMPLE
Array begins:
====================================================================
n\k | 0 1 2 3 4 5
----+---------------------------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 ...
2 | 0 1 6 24 70 165 ...
3 | 0 1 140 4995 65824 489125 ...
4 | 0 1 16456 10763361 1073758336 38147070625 ...
5 | 0 1 8390720 211822552035 281474993496064 74505806274453125 ...
...
MATHEMATICA
{{1}}~Join~Table[Function[n, (k^(n^2) + 2*k^((n^2 + 3 #)/4) + k^((n^2 + #)/2))/4 &[Mod[n, 2] ] ][m - k + 1], {m, 0, 8}, {k, m + 1, 0, -1}] // Flatten (* Michael De Vlieger, Nov 30 2023 *)
PROG
(PARI) T(n, k) = (k^(n^2) + 2*k^((n^2 + 3*(n%2))/4) + k^((n^2 + (n%2))/2))/4
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 14 2021
STATUS
approved