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A380616
Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
4
1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 17, 33, 30, 13, 3, 79, 198, 208, 118, 35, 6, 554, 1571, 1894, 1232, 472, 104, 12, 5283, 16431, 21440, 15545, 6879, 1914, 315, 27, 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65, 966156, 3288821, 4799336, 4019360, 2163112, 787065, 196267, 32857, 3407, 175
OFFSET
0,4
COMMENTS
By duality, also the number of unsensed combinatorial maps with n edges and k faces.
FORMULA
T(n,k) = (A380615(n,k) + A380617(n,k))/2.
EXAMPLE
Triangle begins:
n\k | 1 2 3 4 5 6 7 8 9
----+--------------------------------------------------------------
0 | 1;
1 | 1, 1;
2 | 2, 2, 1;
3 | 5, 8, 5, 2;
4 | 17, 33, 30, 13, 3;
5 | 79, 198, 208, 118, 35, 6;
6 | 554, 1571, 1894, 1232, 472, 104, 12;
7 | 5283, 16431, 21440, 15545, 6879, 1914, 315, 27;
8 | 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65;
...
CROSSREFS
Row sums are A214816.
Main diagonal is A006082(n+1).
Columns 1..3 are A054499, A380620, A380621.
Cf. A053979 (rooted), A277741 (planar), A380615 (sensed), A380617 (achiral).
Sequence in context: A342722 A344528 A380617 * A380615 A329429 A387609
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 28 2025
STATUS
approved