A379430
Array read by antidiagonals: A(n,k) is the number of sensed planar maps with n vertices and k faces, n >= 1, k >= 1.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 14, 23, 14, 3, 6, 42, 108, 108, 42, 6, 14, 140, 501, 761, 501, 140, 14, 34, 473, 2264, 4744, 4744, 2264, 473, 34, 95, 1670, 10087, 27768, 38495, 27768, 10087, 1670, 95, 280, 5969, 44310, 153668, 279698, 279698, 153668, 44310, 5969, 280
Offset: 1
Array begins:
=========================================================
n\k | 1 2 3 4 5 6 7 8 ...
----+----------------------------------------------------
1 | 1 1 1 2 3 6 14 34 ...
2 | 1 2 5 14 42 140 473 1670 ...
3 | 1 5 23 108 501 2264 10087 44310 ...
4 | 2 14 108 761 4744 27768 153668 ...
5 | 3 42 501 4744 38495 279698 ...
6 | 6 140 2264 27768 279698 ...
7 | 14 473 10087 153668 ...
8 | 34 1670 44310 ...
...
As a triangle, rows give the number of edges (first row is 0 edges):
1;
1, 1;
1, 2, 1;
2, 5, 5, 2;
3, 14, 23, 14, 3;
6, 42, 108, 108, 42, 6;
14, 140, 501, 761, 501, 140, 14;
34, 473, 2264, 4744, 4744, 2264, 473, 34;
95, 1670, 10087, 27768, 38495, 27768, 10087, 1670, 95;
...
A384963
Triangle read by rows: T(n,k) is the number of embeddings on the sphere of connected simple planar graphs with n nodes and k faces, n >= 1, k=1..max(1,2*n-4).
Original entry on oeis.org
1, 1, 1, 1, 2, 2, 1, 1, 3, 7, 7, 5, 2, 1, 6, 22, 42, 49, 35, 18, 5, 2, 12, 76, 237, 442, 510, 412, 218, 84, 18, 5, 27, 271, 1293, 3539, 6205, 7482, 6318, 3833, 1623, 485, 88, 14, 65, 1001, 6757, 25842, 63254, 106985, 129782, 115988, 76582, 37421, 13111, 3228, 489, 50
Offset: 1
Triangle begins:
1;
1;
1, 1;
2, 2, 1, 1,
3, 7, 7, 5, 2, 1;
6, 22, 42, 49, 35, 18, 5, 2;
12, 76, 237, 442, 510, 412, 218, 84, 18, 5;
27, 271, 1293, 3539, 6205, 7482, 6318, 3833, 1623, 485, 88, 14;
...
A384966
Number of sensed simple planar maps with n vertices and 2 faces.
Original entry on oeis.org
0, 0, 1, 2, 8, 29, 113, 444, 1763, 6951, 27395, 107672, 422330, 1654180, 6472518, 25308760, 98923442, 386589398, 1510737079, 5904291401, 23079308104, 90236258057, 352908128341, 1380632536468, 5403055984114, 21152009997924, 82835786189975, 324518950873991, 1271797441923614, 4985982054721119
Offset: 1
-
seq(n)={my(c(d)=(1-sqrt(1-4*x^d + O(x*x^(n+d))))/(2*x^d)); Vec(1/(1 - x*c(2)) - x*(c(1)^2 + c(2)) - x^2*(c(1)^4 + 3*c(2)^2)/2 - 1 - sum(k=1, n, log(2 - c(k))*eulerphi(k)/k), -n)/2}
A384965
Number of sensed simple planar maps with n vertices.
Original entry on oeis.org
1, 1, 2, 6, 28, 253, 3461, 58963, 1139866, 23952568, 534729502, 12511055327, 303919972592, 7613826460120
Offset: 1
Showing 1-4 of 4 results.
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