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A358933 Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z.

%I A358933 #17 May 02 2023 08:37:16
%S A358933 1,0,0,0,2,0,2,2,4,2,10,8,14,18,36,34,66,88,136,170,292,382,578,818,
%T A358933 1244,1692,2576,3676,5400,7654,11412,16284,23852,34448,50396,72472,
%U A358933 106046,153556,223458,323430,471644,683046,993958,1442138,2097830,3042314,4424880
%N A358933 Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z.
%H A358933 Alois P. Heinz, <a href="/A358933/b358933.txt">Table of n, a(n) for n = 0..2000</a>
%H A358933 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A358933 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 5, 2, 10, -4, -7, -35, -26, -34, 13, 43, 94, 115, 51, 30, -124, -99, -276, -52, -131, 182, 128, 298, 189, 71, -30, -118, -118, -96, -56, -8).
%F A358933 G.f.: (x-1)*(x^2 +x +1)*(4*x^26 +28*x^25 +44*x^24 +29*x^23 +x^22 -36*x^21 -49*x^20 -45*x^19 -61*x^18 +15*x^17 -7*x^16 +60*x^15 +x^14 +59*x^13 -11*x^12 +10*x^11 -37*x^10 -25*x^8 +x^7 -2*x^6 +10*x^5 +4*x^3 -1) / (8*x^32 +56*x^31 +96*x^30 +118*x^29 +118*x^28 +30*x^27 -71*x^26 -189*x^25 -298*x^24 -128*x^23 -182*x^22 +131*x^21 +52*x^20 +276*x^19 +99*x^18 +124*x^17 -30*x^16 -51*x^15 -115*x^14 -94*x^13 -43*x^12 -13*x^11 +34*x^10 +26*x^9 +35*x^8 +7*x^7 +4*x^6 -10*x^5 -2*x^4 -5*x^3 +1).
%e A358933 a(7) = 2:
%e A358933   ._____________.    ._____________.
%e A358933   | | ._. | ._. |    | ._. | ._. | |
%e A358933   | |_| |_|_| |_|    |_| |_|_| |_| |
%e A358933   |_. |___. |_. |    | ._| .___| ._|
%e A358933   | |_| | |_| | |    | | |_| | |_| |
%e A358933   |_____|_____|_|    |_|_____|_____|   .
%e A358933 .
%Y A358933 Cf. A174249, A343529, A349187, A352421, A361250.
%K A358933 nonn,easy
%O A358933 0,5
%A A358933 _Alois P. Heinz_, Dec 06 2022