A232622 Number of incongruent domino tilings of the 3 X (2n) board.

1, 2, 5, 14, 46, 156, 561, 2037, 7525, 27874, 103741, 386386, 1440946, 5374772, 20054945, 74835209, 279273961, 1042224066, 3889577781, 14515950582, 54174058390, 202179773644, 754544416081, 2815995989821, 10509437228941, 39221745831842, 146377537461485

Offset: 0

Author

R. J. Mathar, Nov 27 2013

Keywords

• nonn

Comments

Analog to A060312, which counts tilings of the 2 X n board.

Sequence A068928 counts the smaller set of the incongruent tilings of 3 X (2n) without points where 4 tiles meet.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• R. J. Mathar, Paving rectangular regions with rectangular tiles: tatami and non-tatami tilings, arXiv:1311.6135 [math.CO], 2013, Table 10.

Crossrefs

Cf. A060312, A068928.

Formula

Conjecture: G.f.: ( -1+3*x+4*x^2-10*x^3+4*x^5-x^6 ) / ( (x-1)*(x^2-4*x+1)*(x^4-4*x^2+1) ).

a(n) = 5a(n-1)-a(n-2)-19a(n-3)+19a(n-4)+a(n-5)-5a(n-6)+a(n-7) for n > 6. - Conjectured by Jean-François Alcover, Jan 21 2019

Extensions

Terms a(16) and beyond from Andrew Howroyd, Sep 20 2017