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Number of tilings of a 5 X n rectangle using dominoes and right trominoes.
2

%I #7 Aug 19 2024 08:42:25

%S 1,0,24,140,2319,21272,262191,2746048,31411948,342302244,3830482893,

%T 42241878920,469601959777,5197411955932,57664560160890,

%U 638914582091712,7084373947760105,78520055192688696,870480364546718647,9649003719594586976,106963676725852631636

%N Number of tilings of a 5 X n rectangle using dominoes and right trominoes.

%H Alois P. Heinz, <a href="/A219988/b219988.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (6, 76, -182, -590, 2722, -6151, -1636, 17717, -15910, -482, 10814, -4832, -4330, -5915, 13616, -8422, 2920, -216, -20).

%F G.f.: see Maple program.

%p gf:= (2*x^18 +52*x^17 -358*x^16 +1396*x^15 -3682*x^14 +4644*x^13 -2629*x^12 -1426*x^11 +906*x^10 +4146*x^9 -2315*x^8 -2804*x^7 +4106*x^6 -1636*x^5 +245*x^4 +178*x^3 -52*x^2 -6*x +1) /

%p (20*x^19 +216*x^18 -2920*x^17 +8422*x^16 -13616*x^15 +5915*x^14 +4330*x^13 +4832*x^12 -10814*x^11 +482*x^10 +15910*x^9 -17717*x^8 +1636*x^7 +6151*x^6 -2722*x^5 +590*x^4 +182*x^3 -76*x^2 -6*x +1):

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

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

%Y Column k=5 of A219987.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 02 2012