A380616 - OEIS

%I #6 Jan 28 2025 20:51:24

%S 1,1,1,2,2,1,5,8,5,2,17,33,30,13,3,79,198,208,118,35,6,554,1571,1894,

%T 1232,472,104,12,5283,16431,21440,15545,6879,1914,315,27,65346,213831,

%U 296952,233027,115134,37311,7881,1021,65,966156,3288821,4799336,4019360,2163112,787065,196267,32857,3407,175

%N Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

%C By duality, also the number of unsensed combinatorial maps with n edges and k faces.

%F T(n,k) = (A380615(n,k) + A380617(n,k))/2.

%e Triangle begins:

%e n\k |     1       2       3       4       5      6     7     8   9

%e ----+--------------------------------------------------------------

%e   0 |     1;

%e   1 |     1,      1;

%e   2 |     2,      2,      1;

%e   3 |     5,      8,      5,      2;

%e   4 |    17,     33,     30,     13,      3;

%e   5 |    79,    198,    208,    118,     35,     6;

%e   6 |   554,   1571,   1894,   1232,    472,   104,   12;

%e   7 |  5283,  16431,  21440,  15545,   6879,  1914,  315,   27;

%e   8 | 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65;

%e   ...

%Y Row sums are A214816.

%Y Main diagonal is A006082(n+1).

%Y Columns 1..3 are A054499, A380620, A380621.

%Y Cf. A053979 (rooted), A277741 (planar), A380615 (sensed), A380617 (achiral).

%K nonn,tabl

%O 0,4

%A _Andrew Howroyd_, Jan 28 2025