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

%I A219947 #10 Aug 21 2024 09:57:48
%S A219947 1,0,5,8,37,136,545,2376,10534,46824,212926,961552,4374949,19888832,
%T A219947 90570555,412561096,1880381253,8572076760,39086502817,178240531672,
%U A219947 812868845530,3707227380920,16907856403612,77113848855920,351705509804137,1604084309231360
%N A219947 Number of tilings of a 6 X n rectangle using right trominoes and 2 X 2 tiles.
%H A219947 Alois P. Heinz, <a href="/A219947/b219947.txt">Table of n, a(n) for n = 0..500</a>
%H A219947 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A219947 G.f.: see Maple program.
%e A219947 a(2) = 5, because there are 5 tilings of a 6 X 2 rectangle using right trominoes and 2 X 2 tiles:
%e A219947 .___.  .___.  .___.  .___.  .___.
%e A219947 | . |  | ._|  | ._|  |_. |  |_. |
%e A219947 |___|  |_| |  |_| |  | |_|  | |_|
%e A219947 | . |  |___|  |___|  |___|  |___|
%e A219947 |___|  | ._|  |_. |  | ._|  |_. |
%e A219947 | . |  |_| |  | |_|  |_| |  | |_|
%e A219947 |___|  |___|  |___|  |___|  |___|
%p A219947 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) /
%p A219947 (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):
%p A219947 a:= n-> coeff (series (gf, x, n+1), x, n):
%p A219947 seq(a(n), n=0..30);
%Y A219947 Column k=6 of A219946.
%K A219947 nonn
%O A219947 0,3
%A A219947 _Alois P. Heinz_, Dec 01 2012