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%I #8 Jan 22 2024 15:58:24
%S 1,15,106,582,2952,14488,69982,335356,1600624,7624266,36279784,
%T 172546968,820420150,3900386212,18541702744,88140749906,418982915000,
%U 1991645550032,9467293435654,45002706816100,213919774521224,1016864234903874,4833646472767104
%N Number of fixed polyominoes without holes that have a width of n and height of 3.
%H Andrew Howroyd, <a href="/A293263/b293263.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (10,-34,49,-29,2,10,-5,-2).
%F a(n) = 10*a(n-1) - 34*a(n-2) + 49*a(n-3) - 29*a(n-4) + 2*a(n-5) + 10*a(n-6) - 5*a(n-7) - 2*a(n-8) for n > 9.
%F G.f.: x*(1 + 5*x - 10*x^2 - 17*x^3 + 30*x^4 - 5*x^5 - 14*x^6 + x^7 + x^8)/((1 - x)*(1 - 2*x - x^2)*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)).
%t LinearRecurrence[{10,-34,49,-29,2,10,-5,-2},{1,15,106,582,2952,14488,69982,335356,1600624},30] (* _Harvey P. Dale_, Jan 22 2024 *)
%o (PARI) Vec((1 + 5*x - 10*x^2 - 17*x^3 + 30*x^4 - 5*x^5 - 14*x^6 + x^7 + x^8)/((1 - x)*(1 - 2*x - x^2)*(1 - 7*x + 12*x^2 - 7*x^3 + 3*x^4 + 2*x^5)) + O(x^40));
%Y Row 3 of A232103.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Oct 04 2017
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