cp's OEIS Frontend

A341923 Array read by antidiagonals: T(n,k) is the number of 3-connected triangulations of a disk up to orientation-preserving isomorphisms with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.

%I A341923 #9 Mar 13 2021 20:27:38
%S A341923 1,1,1,1,2,5,1,2,10,24,1,3,16,60,133,1,3,28,122,386,846,1,4,39,242,
%T A341923 925,2652,5661,1,4,58,419,2039,7066,18914,39556,1,5,78,711,4101,17138,
%U A341923 54560,139264,286000,1,5,106,1128,7801,38166,142802,426462,1048947,2123329
%N A341923 Array read by antidiagonals: T(n,k) is the number of 3-connected triangulations of a disk up to orientation-preserving isomorphisms with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.
%C A341923 The initial terms of this sequence can also be computed using the tool "plantri", in particular the command "./plantri -u -v -o -P [n]" will compute values for a diagonal.
%H A341923 Andrew Howroyd, <a href="/A341923/b341923.txt">Table of n, a(n) for n = 1..1275</a>
%H A341923 G. Brinkmann and B. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">Plantri (program for generation of certain types of planar graph)</a>
%e A341923 Array begins:
%e A341923 =====================================================
%e A341923 n\k |     3      4      5       6       7       8
%e A341923 ----+------------------------------------------------
%e A341923   1 |     1      1      1       1       1       1 ...
%e A341923   2 |     1      2      2       3       3       4 ...
%e A341923   3 |     5     10     16      28      39      58 ...
%e A341923   4 |    24     60    122     242     419     711 ...
%e A341923   5 |   133    386    925    2039    4101    7801 ...
%e A341923   6 |   846   2652   7066   17138   38166   79908 ...
%e A341923   7 |  5661  18914  54560  142802  345099  782210 ...
%e A341923   8 | 39556 139264 426462 1188412 3067938 7433635 ...
%e A341923   ...
%o A341923 (PARI) A341923Array(8,6) \\ See links in A342053 for program file.
%Y A341923 Columns k=3..6 are A002709, A341924, A341925, A341926.
%Y A341923 Antidiagonal sums are A342052.
%Y A341923 Cf. A262586 (2-connected), A341856 (rooted), A342053 (unrooted).
%K A341923 nonn,tabl
%O A341923 1,5
%A A341923 _Andrew Howroyd_, Feb 26 2021