OFFSET
1,2
COMMENTS
A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
LINKS
E. Barcucci, S. Brunetti, and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
E. Barcucci, A. Del Lungo, and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
FORMULA
EXAMPLE
a(2)=3 because the deco polyominoes of height 2 are the horizontal and vertical dominoes, having, respectively, 1 and 2 rows.
MAPLE
with(linalg): a:=proc(i, j) if i=j then i elif i>j then 1 else 0 fi end: p:=proc(Q) local n, A, b, w, QQ: n:=degree(Q): A:=matrix(n, n, a): b:=j->coeff(Q, t, j): w:=matrix(n, 1, b): QQ:=multiply(A, w): sort(expand(add(QQ[k, 1]*t^k, k=1..n)+t*Q)): end: P[1]:=t: for n from 2 to 22 do P[n]:=p(P[n-1]) od: seq(subs(t=1, diff(P[n], t)), n=1..22);
MATHEMATICA
(* T is A121692 *)
T[n_, k_] := T[n, k] = Which[k == 1, 1, k == n, 1, k > n, 0, True, k*T[n-1, k] + 2*T[n-1, k-1] + Sum[T[n-1, j], {j, 1, k-2}]];
a[n_] := Sum[k*T[n, k], {k, 1, n}];
Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Aug 20 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 17 2006
STATUS
approved