login
A352431
Number T(n,k) of tilings of a 2k X n rectangle using dominoes and 2 X 2 tiles.
4
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 5, 1, 1, 1, 43, 29, 11, 1, 1, 1, 171, 173, 165, 21, 1, 1, 1, 683, 1037, 2773, 593, 43, 1, 1, 1, 2731, 6221, 48605, 17937, 2773, 85, 1, 1, 1, 10923, 37325, 864901, 550969, 205879, 11093, 171, 1
OFFSET
0,9
COMMENTS
Tiling algorithm, see A351322.
The table is read by descending antidiagonals.
If read by columns or rows:
T(n,1) = A001045(n+1);
T(3,k) = A083066(k);
T(n,2) = A352432(n);
T(5,k) = A352433(k).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..860 (first 41 antidiagonals).
Gerhard Kirchner, Maxima code
EXAMPLE
Table T(n,k) begins:
n\k 0 1 2 3 4
-----------------------------------
0: 1 1 1 1 1
1: 1 1 1 1 1
2: 1 3 11 43 171
3: 1 5 29 173 1037
4: 1 11 165 2773 48605
5: 1 21 593 17937 550969
6: 1 43 2773 205879 16231655
7: 1 85 11093 1615993 242436361
8: 1 171 48605 16231655 5811552169
PROG
(Maxima) See "Maxima code" link.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gerhard Kirchner, Mar 17 2022
STATUS
approved