cp's OEIS Frontend

A121554 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k 1-cell columns (0<=k<=n). 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 A121554 #2 Mar 30 2012 17:36:10
%S A121554 1,0,1,1,0,1,2,2,1,1,7,7,6,3,1,30,35,30,18,6,1,157,205,184,117,46,10,
%T A121554 1,972,1392,1304,874,381,101,15,1,6961,10764,10499,7355,3470,1052,197,
%U A121554 21,1,56660,93493,94668,68909,34622,11606,2542,351,28,1,516901,901900
%N A121554 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k 1-cell columns (0<=k<=n). 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 A121554 Row sums are the factorials (A000142). T(n,0)=A001053(n). Sum(k*T(n,k), k=0..n)=A121555(n).
%D A121554 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121554 The row generating polynomials are P(n,t)=Q(n,t,1), where Q(0,t,x)=1 and Q(n,t,x)=Q(n-1,t,1/t)+(tx+n-2)Q(n-1,t,1) for n>=1.
%e A121554 T(2,0)=1, T(2,1)=0, T(2,2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 2 columns with exactly 1 cell.
%e A121554 Triangle starts:
%e A121554 1;
%e A121554 0,1;
%e A121554 1,0,1;
%e A121554 2,2,1,1;
%e A121554 7,7,6,3,1;
%e A121554 30,35,30,18,6,1;
%p A121554 Q[0]:=1: for n from 1 to 10 do Q[n]:=sort(expand(subs(x=1/t,Q[n-1])+(t*x+n-2)*subs(x=1,Q[n-1]))) od: for n from 0 to 10 do P[n]:=subs(x=1,Q[n]) od: for n from 0 to 10 do seq(coeff(P[n],t,j),j=0..n) od; # yields sequence in triangular form
%Y A121554 Cf. A000142, A001053, A121555.
%K A121554 nonn,tabl
%O A121554 0,7
%A A121554 _Emeric Deutsch_, Aug 08 2006