

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 columnconvex 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
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OFFSET

1,4


COMMENTS

Row sums are the factorials (A000142). T(n,0)=A121753 Sum(k*T(n,k), k=0..n1)=A121754(n).


REFERENCES

E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 114.
E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 2942.


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[n1](s,t)+[floor(n/2)*t+floor((n1)/2)*s]Q[n1](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[n1])+(t*floor(n/2)+s*floor((n1)/2))*Q[n1]) 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..n1) 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



