A219947 Number of tilings of a 6 X n rectangle using right trominoes and 2 X 2 tiles.

1, 0, 5, 8, 37, 136, 545, 2376, 10534, 46824, 212926, 961552, 4374949, 19888832, 90570555, 412561096, 1880381253, 8572076760, 39086502817, 178240531672, 812868845530, 3707227380920, 16907856403612, 77113848855920, 351705509804137, 1604084309231360

Offset: 0

Author

Alois P. Heinz, Dec 01 2012

Keywords

• nonn

Examples

			a(2) = 5, because there are 5 tilings of a 6 X 2 rectangle using right trominoes and 2 X 2 tiles:
.___.  .___.  .___.  .___.  .___.
| . |  | ._|  | ._|  |_. |  |_. |
|___|  |_| |  |_| |  | |_|  | |_|
| . |  |___|  |___|  |___|  |___|
|___|  | ._|  |_. |  | ._|  |_. |
| . |  |_| |  | |_|  |_| |  | |_|
|___|  |___|  |___|  |___|  |___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (4, 18, -34, -263, -12, 2014, 2806, -7488, -24088, 1136, 88592, 107125, -137172, -393128, -92654, 725593, 673176, -476620, -1242434, -1310, 781380, 541484, -521244, -141200, -87952, 165952, -11840, 14592, -16640).

Crossrefs

Column k=6 of A219946.

Programs

Maple

gf:= -(6080*x^25 -7104*x^24 -21936*x^23 -4112*x^22 +82016*x^21 +39064*x^20 -139520*x^19 -103312*x^18 +102180*x^17 +165884*x^16 -18076*x^15 -101470*x^14 -41918*x^13 +35248*x^12 +29374*x^11 -1107*x^10 -10608*x^9 -3089*x^8 +1636*x^7 +1092*x^6 -26*x^5 -178*x^4 -22*x^3 +13*x^2 +4*x -1) /
(16640*x^29 -14592*x^28 +11840*x^27 -165952*x^26 +87952*x^25 +141200*x^24 +521244*x^23 -541484*x^22 -781380*x^21 +1310*x^20 +1242434*x^19 +476620*x^18 -673176*x^17 -725593*x^16 +92654*x^15 +393128*x^14 +137172*x^13 -107125*x^12 -88592*x^11 -1136*x^10 +24088*x^9 +7488*x^8 -2806*x^7 -2014*x^6 +12*x^5 +263*x^4 +34*x^3 -18*x^2 -4*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq(a(n), n=0..30);

Formula

G.f.: see Maple program.