cp's OEIS Frontend

A121583 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having k cells in the first two columns (n>=1, k>=1). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

%I A121583 #2 Mar 30 2012 17:36:10
%S A121583 1,0,2,0,1,4,1,0,2,6,10,5,1,0,6,16,29,34,23,11,1,0,24,60,102,148,154,
%T A121583 119,77,35,1,0,120,288,474,668,867,874,719,533,341,155,1,0,720,1680,
%U A121583 2712,3768,4834,5906,5914,5039,4013,2957,1901,875,1,0,5040,11520,18360
%N A121583 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having k cells in the first two columns (n>=1, k>=1). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%C A121583 Row n has 2n-2 terms (n>=2). Row sums are the factorials (A000142). Sum(k*T(n,k), k=0..n)=A121584(n)
%D A121583 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121583 The generating polynomial of row n is P(n,t)=Q(n,t,t), where Q(1,t,s)=t and Q(n,t,s)=tQ(n-1,t,s)+(t^n-t)Q(n-1,s,1)/(t-1) for n>=2.
%e A121583 T(2,2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, each having 2 cells in their first two columns.
%e A121583 Triangle starts:
%e A121583 1;
%e A121583 0,2;
%e A121583 0,1,4,1;
%e A121583 0,2,6,10,5,1;
%e A121583 0,6,16,29,34,23,11,1;
%p A121583 Q[1]:=t: for n from 2 to 9 do Q[n]:=expand(simplify(t*Q[n-1]+(t^n-t)/(t-1)*subs({t=s,s=1},Q[n-1]))) od: for n from 1 to 9 do P[n]:=sort(subs(s=t,Q[n])): od: 1; for n from 1 to 9 do seq(coeff(P[n],t,j),j=1..2*n-2) od; # yields sequence in triangular form
%Y A121583 Cf. A000142, A100822, A121581, A121584.
%K A121583 nonn,tabf
%O A121583 1,3
%A A121583 _Emeric Deutsch_, Aug 11 2006