%I #7 Aug 19 2024 08:43:39

%S 1,1,53,633,15171,262191,5350806,100578811,1973546988,37873593799,

%T 735394314429,14191155767741,274752269763958,5310160930571538,

%U 102725211030603178,1986240719213420369,38415016070710912599,742863889918219971720,14366465865750557446408

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

%H Alois P. Heinz, <a href="/A219989/b219989.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, 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).

%F G.f.: see Maple program.

%p 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

%p +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) /

%p (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

%p -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):

%p a:= n-> coeff (series (gf, x, n+1), x, n):

%p seq (a(n), n=0..30);

%Y Column k=6 of A219987.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 02 2012