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A219947
Number of tilings of a 6 X n rectangle using right trominoes and 2 X 2 tiles.
2
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
0,3
LINKS
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).
FORMULA
G.f.: see Maple program.
EXAMPLE
a(2) = 5, because there are 5 tilings of a 6 X 2 rectangle using right trominoes and 2 X 2 tiles:
.___. .___. .___. .___. .___.
| . | | ._| | ._| |_. | |_. |
|___| |_| | |_| | | |_| | |_|
| . | |___| |___| |___| |___|
|___| | ._| |_. | | ._| |_. |
| . | |_| | | |_| |_| | | |_|
|___| |___| |___| |___| |___|
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);
CROSSREFS
Column k=6 of A219946.
Sequence in context: A187997 A188065 A204676 * A075273 A176859 A176757
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 01 2012
STATUS
approved