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A121298 Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n and height k (1<=k<=n; here by the height of a polyomino one means the number of lines of slope -1 that pass through the centers of the polyomino cells). 1
1, 0, 2, 0, 1, 4, 0, 0, 5, 8, 0, 0, 3, 15, 16, 0, 0, 1, 17, 39, 32, 0, 0, 0, 15, 59, 95, 64, 0, 0, 0, 9, 75, 175, 223, 128, 0, 0, 0, 4, 78, 269, 479, 511, 256, 0, 0, 0, 1, 67, 358, 845, 1247, 1151, 512, 0, 0, 0, 0, 48, 419, 1300, 2461, 3135, 2559, 1024, 0, 0, 0, 0, 29, 432, 1801 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are the odd-subscripted Fibonacci numbers (A001519). Sum of terms in column k = A007808(k). Sum(k*T(n,k),k=0..n)=A121299(n).

LINKS

Table of n, a(n) for n=1..73.

E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos dirigés verticalement convexes, Actes du 31e Séminaire Lotharingien de Combinatoire, Publi. IRMA, Université Strasbourg I (1993).

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

T(n,k) = T(n-1,k-1)+Sum(T(n-k,j), j=1..k-1)+Sum(T(n-j,k-1), j=1..k-1).

EXAMPLE

T(2,2)=2 because we have the vertical and the horizontal dominoes.

Triangle starts:

1;

0,2;

0,1,4;

0,0,5,8;

0,0,3,15,16;

0,0,1,17,39,32;

MAPLE

T:=proc(n, k) if n<=0 or k<=0 then 0 elif n=1 and k=1 then 1 else T(n-1, k-1)+add(T(n-k, j), j=1..k-1)+add(T(n-j, k-1), j=1..k-1) 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, A007808, A121299.

Sequence in context: A061290 A099096 A099089 * A212206 A247489 A208756

Adjacent sequences:  A121295 A121296 A121297 * A121299 A121300 A121301

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 04 2006

STATUS

approved

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Last modified June 24 06:11 EDT 2021. Contains 345416 sequences. (Running on oeis4.)