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A349187 Number of tilings of a 5 X n rectangle using n pentominoes of shapes X, Y, Z.

%I A349187 #13 Apr 30 2022 20:57:50
%S A349187 1,0,0,0,0,6,6,6,2,10,86,118,166,152,372,1394,2450,3866,4946,10160,
%T A349187 26380,50770,86522,131632,251150,548436,1075036,1918294,3205242,
%U A349187 5953962,11962044,23255472,42565706,74859582,138078796,266506794,511327170,947685504,1713749022
%N A349187 Number of tilings of a 5 X n rectangle using n pentominoes of shapes X, Y, Z.
%H A349187 Alois P. Heinz, <a href="/A349187/b349187.txt">Table of n, a(n) for n = 0..3700</a>
%H A349187 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A349187 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,13,7,8,1,-10,-14,-20,-8,-7,-38,-33,-2,0,-5,-16,-11).
%F A349187 G.f.: (x^20 +6*x^19 +5*x^18 +7*x^15 +14*x^14 +7*x^13 +4*x^10 +2*x^9 +x^8 -2*x^7 -x^6 -7*x^5 -3*x^4 +1) / (11*x^20 +16*x^19 +5*x^18 +2*x^16 +33*x^15 +38*x^14 +7*x^13 +8*x^12 +20*x^11 +14*x^10 +10*x^9 -x^8 -8*x^7 -7*x^6 -13*x^5 -3*x^4 +1).
%e A349187 a(5) = 6:
%e A349187   ._________.     ._________.
%e A349187   |_. ._._| |     | |___. ._|
%e A349187   | |_| |_. |     | |_  |_| |
%e A349187   | |_. ._| |     | ._| |_. |
%e A349187   | ._|_| |_| (2) |_| |___| | (4)
%e A349187   |_|_______|     |_______|_|      .
%e A349187 .
%e A349187 a(8) = 2:
%e A349187   ._______________.
%e A349187   |_. | |___. ._| |
%e A349187   | | |___. |_|_. |
%e A349187   | |___| |_|_. | |
%e A349187   | ._| |___. | |_| (2)
%e A349187   |_|_______|_|___|      .
%e A349187 .
%Y A349187 Cf. A174249, A343529.
%K A349187 nonn,easy
%O A349187 0,6
%A A349187 _Alois P. Heinz_, Nov 09 2021