A322498 Number of tilings of a 5 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.

1, 1, 8, 44, 233, 1262, 6523, 34468, 181615, 957006, 5044388, 26575335, 140039124, 737911089, 3888300180, 20488828781, 107962314409, 568889946804, 2997672175041, 15795742092745, 83233076938962, 438583048406589, 2311041500385152, 12177654397383350

Offset: 0

Author

Alois P. Heinz, Dec 12 2018

Keywords

• nonn
• easy

Comments

The shapes of the tiles are:

._.

._. | |

._. | | | |

.. | |. | |.. | |.._.

|| |__| |___| |_____| ... .

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Polyomino
• Index entries for linear recurrences with constant coefficients, signature (1,10,36,93,240,392,551,576,361,324,58,58,57,-76,50,-10).

Crossrefs

Column k=5 of A322494.

Formula

G.f.: (2*x^11 -8*x^10 +4*x^9 -7*x^8 -18*x^7 -29*x^6 -32*x^5 -20*x^4 -10*x^3 -3*x^2+1) / (10*x^16 -50*x^15 +76*x^14 -57*x^13 -58*x^12 -58*x^11 -324*x^10 -361*x^9 -576*x^8 -551*x^7 -392*x^6 -240*x^5 -93*x^4 -36*x^3 -10*x^2 -x+1).