login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..19.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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