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A121299 Sum of the heights of all directed column-convex polyominoes of area 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). 2
1, 4, 14, 47, 149, 458, 1373, 4046, 11765, 33857, 96611, 273760, 771164, 2161352, 6031104, 16764719, 46442640, 128268379, 353296944, 970717966, 2661204271, 7280832780, 19882745230, 54203791062, 147536291969, 400991600305 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

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

a(n) = Sum(k*A121298(n,k), k=1..n). [Corrected by R. J. Mathar, Sep 18 2007]

EXAMPLE

a(2)=4 because the vertical and the horizontal dominoes have altogether 4 diagonals with slope -1.

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: seq(add(k*T(n, k), k=1..n), n=1..15);

CROSSREFS

Cf. A121298.

Sequence in context: A258255 A124805 A121530 * A326346 A046718 A291385

Adjacent sequences:  A121296 A121297 A121298 * A121300 A121301 A121302

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 04 2006

EXTENSIONS

More terms from R. J. Mathar, Sep 18 2007

STATUS

approved

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Last modified April 5 03:52 EDT 2020. Contains 333238 sequences. (Running on oeis4.)