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A335606 The number of fixed n-ominoes with a convex hull of width 3.

%I A335606 #12 Jan 17 2021 02:31:12
%S A335606 1,8,31,95,269,721,1866,4728,11804,29162,71502,174342,423341,1024786,
%T A335606 2474934,5966625,14365256,34550674,83035396,199440433,478814076,
%U A335606 1149133511,2757142136,6613933242,15863281135,38042981575,91225540813,218739876078,524464594304,1257437814143,3014693395137
%N A335606 The number of fixed n-ominoes with a convex hull of width 3.
%C A335606 Obtained from Zeilberger's tables by subtracting the numbers of width <= 3 and of width <= 2.
%H A335606 D. Zeilberger, <a href="https://sites.math.rutgers.edu/~zeilberg/TM/oani2">Series expansion for 2D lattice-animals of globally bounded width</a>
%H A335606 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>
%H A335606 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-4,8,1,2,-8,0,-1,9,-2,-1,-3,1).
%F A335606 a(n) = A308359(n,3).
%F A335606 G.f.: -x^3*(1+x) *(x^10 -x^9 -3*x^8 +2*x^7 -x^6 -2*x^5 +7*x^4 -3*x^3 -5*x^2 +2*x +1) / ( (x-1) *(x^3 +x^2 +x -1) *(x^10 -3*x^9 -x^8 +2*x^6 +x^4 -4*x^3 +3*x -1) ).
%F A335606 a(n)= 5*a(n-1) -6*a(n-2) -4*a(n-3) +8*a(n-4) +a(n-5) +2*a(n-6) -8*a(n-7) -a(n-9) +9*a(n-10) -2*a(n-11) -a(n-12) -3*a(n-13) +a(n-14).
%e A335606 a(3)=1 counts 1 3-omino of shape 1x3.
%e A335606 a(4)=8 counts 8 4-ominoes of shape 2x3.
%e A335606 a(5)=31 counts 6 5-ominoes of shape 2x3 and 25 5-ominoes of shape 3x3.
%e A335606 a(6)=95 counts 1 6-omino of shape 2x3, 44 6-ominoes of shape 3x3 and 50 6-ominoes of shape 4x3.
%t A335606 LinearRecurrence[{5, -6, -4, 8, 1, 2, -8, 0, -1, 9, -2, -1, -3, 1}, {1, 8, 31, 95, 269, 721, 1866, 4728, 11804, 29162, 71502, 174342, 423341, 1024786, 2474934}, 31] (* _Georg Fischer_, Jan 16 2021 *)
%Y A335606 Cf. A308359, A027053 (width 2).
%K A335606 nonn,easy
%O A335606 3,2
%A A335606 _R. J. Mathar_, Jun 15 2020