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A121698 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k columns ending at an even level (1<=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. 3
1, 1, 1, 2, 2, 2, 6, 8, 7, 3, 16, 36, 37, 23, 8, 62, 172, 220, 166, 80, 20, 230, 844, 1383, 1338, 835, 338, 72, 1114, 4796, 9331, 10828, 8265, 4282, 1452, 252, 5268, 27450, 64612, 91023, 85248, 55445, 25158, 7524, 1152, 30702, 181606, 489847, 798355 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are the factorials (A000142). T(n,0)=A121753 Sum(k*T(n,k), k=0..n-1)=A121754(n).

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..49.

FORMULA

The row generating polynomials P[n](s) are given by P[n](s)=Q[n](1,s), where Q[n](t,s) are defined by Q[n](t,s)=Q[n-1](s,t)+[floor(n/2)*t+floor((n-1)/2)*s]Q[n-1](t,s) for n>=2 and Q[1](t,s]=t.

EXAMPLE

T(2,0)=1 and T(2,1)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes, having 0 and 1 columns ending at an even level, respectively.

Triangle starts:

1;

1,1;

2,2,2;

6,8,7,3;

16,36,37,23,8;

62,172,220,166,80,20;

MAPLE

Q[1]:=t: for n from 2 to 10 do Q[n]:=expand(subs({t=s, s=t}, Q[n-1])+(t*floor(n/2)+s*floor((n-1)/2))*Q[n-1]) od: for n from 1 to 10 do P[n]:=sort(subs(t=1, Q[n])) od: for n from 0 to 10 do seq(coeff(P[n], s, j), j=0..n-1) od; # yields sequence in triangular form

CROSSREFS

Cf. A000142, A121753, A121754, A121697.

Sequence in context: A151694 A298745 A323860 * A087482 A137227 A323862

Adjacent sequences:  A121695 A121696 A121697 * A121699 A121700 A121701

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 23 2006

STATUS

approved

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)