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 A121694 Sum of the vertical heights (i.e., number of rows) of all deco polyominoes of height n. 1
 1, 3, 12, 61, 377, 2734, 22671, 211035, 2175754, 24592551, 302295925, 4014475756, 57277225309, 873819665135, 14195291340656, 244657733062761, 4459137940238245, 85694418205589534, 1731893273528613811 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = Sum_{k=1..n} k*A121692(n,k). a(n) = Sum_{k=1..n} k*T(n,k), where T(n,k) (A121692) is defined by T(n,1)=1; T(n,n)=1; T(n,k) = k*T(n-1,k) + 2*T(n-1,k-1) + Sum_{j=1..k-2} T(n-1,j) for k <= n; T(n,k)=0 for k > n. 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); CROSSREFS Cf. A121692. Sequence in context: A331607 A235802 A317169 * A331616 A158691 A038171 Adjacent sequences:  A121691 A121692 A121693 * A121695 A121696 A121697 KEYWORD nonn AUTHOR Emeric Deutsch, Aug 17 2006 STATUS approved

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Last modified December 2 05:03 EST 2020. Contains 338865 sequences. (Running on oeis4.)