This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006801 M1440 #27 Jul 08 2025 16:55:18
%S A006801 1,2,5,13,34,90,239,635,1689,4494,11960,31832,84727,225524,600302,
%T A006801 1597904,4253371,11321838,30137079,80220557,213535632,568401380,
%U A006801 1513003529
%N A006801 Number of 2-dimensional directed compact animals of size n.
%C A006801 Directed d- diagonally convex polyominoes. - _David Bevan_, Mar 15 2011
%D A006801 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006801 V. K. Bhat et al., <a href="https://doi.org/10.1088/0305-4470/19/16/024">Enumeration of directed compact site animals in two dimensions</a>, J. Phys. A 19 (1986), 3261-3265.
%e A006801 a(3)=5: the six fixed trominoes excluding one orientation of the L tromino. - _David Bevan_, Mar 15 2011
%t A006801 a[n_,k_]:=0/;n<1||k<1||k(k+1)/2>n; a[1,1]=1; a[n_,k_]:=a[n,k]=Sum[(j-k+2)a[n-k,j],{j,k-1,n-k}]; a[n_]:=Sum[a[n,k],{k,n}]; Array[a,30] (* _David Bevan_, Mar 15 2011 *)
%Y A006801 Cf. A187276 (d- diagonally convex polyominoes).
%K A006801 nonn,more
%O A006801 1,2
%A A006801 _N. J. A. Sloane_
%E A006801 Name and offset corrected, and more terms added by _David Bevan_, Mar 15 2011