A219989 Number of tilings of a 6 X n rectangle using dominoes and right trominoes.

1, 1, 53, 633, 15171, 262191, 5350806, 100578811, 1973546988, 37873593799, 735394314429, 14191155767741, 274752269763958, 5310160930571538, 102725211030603178, 1986240719213420369, 38415016070710912599, 742863889918219971720, 14366465865750557446408

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

G.f.: see Maple program.

Maple

gf:= (144*x^33 -16884*x^32 -172332*x^31 +37368*x^30 +1446802*x^29 +1843379*x^28 +3892967*x^27 -4330825*x^26 -7997135*x^25 +2597250*x^24 +20344704*x^23 +1683173*x^22 -102335065*x^21 -11071738*x^20
+108818264*x^19 +20558409*x^18 -23625389*x^17 -12070930*x^16 +22478862*x^15 -21548636*x^14 -14801976*x^13 +5193535*x^12 +6957072*x^11 +1167575*x^10 -1273601*x^9 -201269*x^8 -40977*x^7 +40180*x^6 -17860*x^5 +2794*x^4 +1014*x^3 -158*x^2 -12*x +1) /
(3524*x^34 -83096*x^33 -106664*x^32 +1460964*x^31 +2491759*x^30 -10066106*x^29 +16579985*x^28 +52063405*x^27 -114723369*x^26 -189274778*x^25 +179637116*x^24 +795173421*x^23 -341486785*x^22
-1428249826*x^21 +545218943*x^20 +815649290*x^19 -214359517*x^18 -112821018*x^17 -21043915*x^16 +130787555*x^15 -134747676*x^14 -11727284*x^13 +9444877*x^12 +20759881*x^11 -561821*x^10 -1798776*x^9 -498954*x^8 -78279*x^7 +59713*x^6 -29776*x^5 +5078*x^4 +1268*x^3 -198*x^2 -13*x +1):
a:= n-> coeff (series (gf, x, n+1), x, n):
seq (a(n), n=0..30);

Crossrefs

Column k=6 of A219987.

Sequence in context: A245589 A177141 A096707 * A027007 A142780 A289808

Adjacent sequences: A219986 A219987 A219988 * A219990 A219991 A219992

Keyword

nonn

Author

Alois P. Heinz, Dec 02 2012

Status

approved