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%I #9 Jul 22 2022 13:27:31
%S 0,0,1,12,57,216,741,2412,7617,23616,72381,220212,666777,2012616,
%T 6062421,18236412,54807537,164619216,494250861,1483539012,4452189897,
%U 13359715416,40085437701,120268896012,360831853857,1082545893216
%N Number of deco polyominoes of height n and vertical height 3 (i.e., having 3 rows).
%C A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%H E. Barcucci, S. Brunetti and F. Del Ristoro, <a href="http://www.numdam.org/item?id=ITA_2000__34_1_1_0">Succession rules and deco polyominoes</a>, Theoret. Informatics Appl., 34, 2000, 1-14.
%H E. Barcucci, A. Del Lungo and R. Pinzani, <a href="http://dx.doi.org/10.1016/0304-3975(95)00199-9">"Deco" polyominoes, permutations and random generation</a>, Theoretical Computer Science, 159, 1996, 29-42.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = A121692(n,3).
%F a(n) = 23*3^(n-3)/2 + 3/2 - 3*2^(n-1) for n >= 3.
%F Recurrence relation: a(n) = 3(a(n-1) + 2^(n-2) - 1) for n >= 4, a(1) = a(2) = 0, a(3) = 1.
%F G.f. = x^3*(1+6x-4x^2)/((1-x)(1-2x)(1-3x)).
%p a[1]:=0: a[2]:=0: a[3]:=1: for n from 4 to 30 do a[n]:=3*(a[n-1]+2^(n-2)-1) od: seq(a[n],n=1..30);
%Y Cf. A121692.
%K nonn,easy
%O 1,4
%A _Emeric Deutsch_, Aug 17 2006
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