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A220056 Number of tilings of a 6 X n rectangle using right trominoes and 1 X 1 tiles.

%I A220056 #7 Aug 20 2024 09:28:41
%S A220056 1,1,241,3895,151817,4134881,128938297,3814023955,115136505933,
%T A220056 3448441154503,103598912114381,3108676107844557,93324146271938457,
%U A220056 2801146229279170843,84082823432914559453,2523871643346500063787,75758559732310254661669,2274020749613202850958405
%N A220056 Number of tilings of a 6 X n rectangle using right trominoes and 1 X 1 tiles.
%H A220056 Alois P. Heinz, <a href="/A220056/b220056.txt">Table of n, a(n) for n = 0..300</a>
%H A220056 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (13, 523, 607, -29450, -10786, 530937, 37118, -5299837, 4432537, 25090652, -45228345, -26901436, 118554222, -46195161, -104188994, 68370580, 80969102, -53775823, -89810738, 93989108, 11698064, -39110100, 3529824, 6795568, 641184, -988592, -441952, 102080, 49664, -3072).
%F A220056 G.f. see Maple program.
%p A220056 gf:= -(128*x^27 -2784*x^26 +11984*x^25 -8672*x^24 -7128*x^23 -34144*x^22 -125640*x^21 +760596*x^20 -718466*x^19 -174758*x^18 +2760675*x^17 -10918043*x^16 +15110507*x^15 -1068879*x^14 -13774618*x^13 +9742272*x^12 +298116*x^11 -1535703*x^10 -168489*x^9 +78558*x^8 +130467*x^7 +2413*x^6 -18124*x^5 -3982*x^4 +368*x^3 +295*x^2 +12*x -1) /
%p A220056 (3072*x^30 -49664*x^29 -102080*x^28 +441952*x^27 +988592*x^26 -641184*x^25 -6795568*x^24 -3529824*x^23 +39110100*x^22 -11698064*x^21 -93989108*x^20 +89810738*x^19 +53775823*x^18 -80969102*x^17 -68370580*x^16 +104188994*x^15 +46195161*x^14 -118554222*x^13 +26901436*x^12 +45228345*x^11 -25090652*x^10 -4432537*x^9 +5299837*x^8 -37118*x^7 -530937*x^6 +10786*x^5 +29450*x^4 -607*x^3 -523*x^2 -13*x +1):
%p A220056 a:= n-> coeff (series (gf, x, n+1), x, n):
%p A220056 seq(a(n), n=0..30);
%Y A220056 Column k=6 of A220054.
%K A220056 nonn
%O A220056 0,3
%A A220056 _Alois P. Heinz_, Dec 03 2012