

A121301


Triangle read by rows: T(n,k) is the number of directed columnconvex polyominoes of area n and having k cells in the shortest column (1<=k<=n).


1



1, 1, 1, 4, 0, 1, 10, 2, 0, 1, 28, 5, 0, 0, 1, 75, 10, 3, 0, 0, 1, 202, 23, 7, 0, 0, 0, 1, 540, 57, 8, 4, 0, 0, 0, 1, 1440, 129, 18, 9, 0, 0, 0, 0, 1, 3828, 294, 43, 10, 5, 0, 0, 0, 0, 1, 10153, 680, 90, 11, 11, 0, 0, 0, 0, 0, 1, 26875, 1557, 178, 28, 12, 6, 0, 0, 0, 0, 0, 1, 71021, 3546
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OFFSET

1,4


COMMENTS

Row sums are the oddsubscripted Fibonacci numbers (A001519). T(n,1)=fibonacci(2n1)A121469(n,0) (obviously, since A121469(n,k) is the number of directed columnconvex polyominoes of area n and having k 1cell columns). T(n,n)=1.


LINKS

Table of n, a(n) for n=1..80.
E. Barcucci, R. Pinzani and R. Sprugnoli, Directed columnconvex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282298.


FORMULA

G.f. of column k is f[k]f[k+1], where f[k]=z^k*(1z)/(z^22*z+1+z^(1+k)*kk*z^kz^(1+k)) is the g.f. for directed columnconvex polyominoes whose columns have height at least k.


EXAMPLE

Triangle starts:
1;
1,1;
4,0,1;
10,2,0,1;
28,5,0,0,1;
75,10,3,0,0,1;
202,23,7,0,0,0,1;


MAPLE

f:=k>z^k*(1z)/(z^22*z+1+z^(1+k)*kk*z^kz^(1+k)): T:=proc(n, k) if k<=n then coeff(series(f(k)f(k+1), z=0, 15), z, n) else 0 fi end: for n from 1 to 13 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form


CROSSREFS

Cf. A001519, A121469, A121300.
Sequence in context: A199786 A189245 A289222 * A059056 A127153 A178979
Adjacent sequences: A121298 A121299 A121300 * A121302 A121303 A121304


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Aug 04 2006


STATUS

approved



