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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (13, 198, -1268, -5078, 29776, -59713, 78279, 498954, 1798776, 561821, -20759881, -9444877, 11727284, 134747676, -130787555, 21043915, 112821018, 214359517, -815649290, -545218943, 1428249826, 341486785, -795173421, -179637116, 189274778, 114723369, -52063405, -16579985, 10066106, -2491759, -1460964, 106664, 83096, -3524).
Crossrefs
Column k=6 of A219987.
Programs
-
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);
Formula
G.f.: see Maple program.