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A121300 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and having k cells in the longest column (1<=k<=n). 1
1, 1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 12, 5, 1, 1, 31, 35, 15, 6, 1, 1, 63, 95, 48, 18, 7, 1, 1, 127, 249, 145, 58, 21, 8, 1, 1, 255, 640, 418, 181, 68, 24, 9, 1, 1, 511, 1615, 1180, 545, 213, 78, 27, 10, 1, 1, 1023, 4026, 3279, 1593, 649, 245, 88, 30, 11, 1, 1, 2047, 9944, 8981 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are the odd-subscripted Fibonacci numbers (A001519). T(n,1)=1; T(n,2)=2^(n-1)-1=A000225(n-1); T(n,n)=1.

LINKS

Table of n, a(n) for n=1..70.

E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.

FORMULA

G.f. of column k is f[k]-f[k-1], where f[k]=Sum(z^i, i=1..k)/[1-Sum(jz^j, j=1..k)] is the g.f. for directed column-convex polyominoes whose columns have height at most k.

EXAMPLE

Triangle starts:

1;

1,1;

1,3,1;

1,7,4,1;

1,15,12,5,1;

1,31,35,15,6,1;

MAPLE

f:=k->sum(z^i, i=1..k)/(1-sum(j*z^j, j=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 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

CROSSREFS

Cf. A001519, A000225.

Sequence in context: A126713 A140068 A179745 * A283595 A128119 A158198

Adjacent sequences:  A121297 A121298 A121299 * A121301 A121302 A121303

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 04 2006

STATUS

approved

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Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)