cp's OEIS Frontend

A308300 T(n,k) is the number of simply connected square animals with n cells and k internal vertices (0 <= k <= A083479(n)), triangle read by rows.

%I A308300 #28 Dec 11 2021 04:54:56
%S A308300 1,1,2,4,1,11,1,27,7,1,82,21,4,250,90,21,2,815,334,89,9,1,2685,1311,
%T A308300 391,67,6,9072,4978,1674,324,45,1,30889,19030,7089,1630,275,23,1,
%U A308300 106290,72082,29433,7629,1498,174,11
%N A308300 T(n,k) is the number of simply connected square animals with n cells and k internal vertices (0 <= k <= A083479(n)), triangle read by rows.
%H A308300 John Mason, <a href="/A308300/b308300.txt">Table of n, a(n) for n = 1..95, rows 1..18</a>
%H A308300 Elena V. Konstantinova, <a href="https://www.researchgate.net/publication/228555054">The constructive enumeration of square animals</a>, POSTECH 10 (2000).
%H A308300 Elena V. Konstantinova and Maxim V. Vidyuk, <a href="http://dx.doi.org/10.1021/ci025659y">Discriminating tests of information and topological indices. Animals and trees</a>, J. Chem. Inf. Comput. Sci. 43 (2003), 1860-1871, Table 2.
%e A308300 The table starts:
%e A308300        1;
%e A308300        1;
%e A308300        2;
%e A308300        4,     1;
%e A308300       11,     1;
%e A308300       27,     7,     1;
%e A308300       82,    21,     4;
%e A308300      250,    90,    21,    2;
%e A308300      815,   334,    89,    9,    1;
%e A308300     2685,  1311,   391,   67,    6;
%e A308300     9072,  4978,  1674,  324,   45,   1;
%e A308300    30889, 19030,  7089, 1630,  275,  23,  1;
%e A308300   106290, 72082, 29433, 7629, 1498, 174, 11;
%e A308300   ...
%Y A308300 Cf. A000104 (row sums), A350030 (first column of this sequence).
%K A308300 nonn,tabf
%O A308300 1,3
%A A308300 _R. J. Mathar_, May 19 2019