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%I #12 Dec 29 2023 12:04:46
%S 1,4,14,47,149,458,1373,4046,11765,33857,96611,273760,771164,2161352,
%T 6031104,16764719,46442640,128268379,353296944,970717966,2661204271,
%U 7280832780,19882745230,54203791062,147536291969,400991600305
%N 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.
%H E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, <a href="http://www.mat.univie.ac.at/~slc/opapers/s31barc.html">La hauteur des polyominos dirigés verticalement convexes</a>, Actes du 31e Séminaire Lotharingien de Combinatoire, Publi. IRMA, Université Strasbourg I (1993).
%H E. Barcucci, R. Pinzani and R. Sprugnoli, <a href="http://dx.doi.org/10.1007/3-540-56610-4_71">Directed column-convex polyominoes by recurrence relations</a>, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
%F a(n) = Sum(k*A121298(n,k), k=1..n). [Corrected by _R. J. Mathar_, Sep 18 2007]
%e a(2)=4 because the vertical and the horizontal dominoes have altogether 4 diagonals with slope -1.
%p 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);
%Y Cf. A121298.
%K nonn
%O 1,2
%A _Emeric Deutsch_, Aug 04 2006
%E More terms from _R. J. Mathar_, Sep 18 2007
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