A232622 - OEIS

%I #15 Jan 21 2019 06:10:52

%S 1,2,5,14,46,156,561,2037,7525,27874,103741,386386,1440946,5374772,

%T 20054945,74835209,279273961,1042224066,3889577781,14515950582,

%U 54174058390,202179773644,754544416081,2815995989821,10509437228941,39221745831842,146377537461485

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

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

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

%H Andrew Howroyd, <a href="/A232622/b232622.txt">Table of n, a(n) for n = 0..200</a>

%H R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving rectangular regions with rectangular tiles: tatami and non-tatami tilings</a>, arXiv:1311.6135 [math.CO], 2013, Table 10.

%F 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) ).

%F 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

%Y Cf. A060312, A068928.

%K nonn

%O 0,2

%A _R. J. Mathar_, Nov 27 2013

%E Terms a(16) and beyond from _Andrew Howroyd_, Sep 20 2017