A352431 Number T(n,k) of tilings of a 2k X n rectangle using dominoes and 2 X 2 tiles.

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

Cf. A351322, A001045, A083066, A352432, A352433.

Sequence in context: A064085 A256692 A228637 * A362783 A152795 A338817

Adjacent sequences: A352428 A352429 A352430 * A352432 A352433 A352434

Keyword

nonn,tabl

Author

Gerhard Kirchner, Mar 17 2022

Status

approved