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A343870
Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) planar graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).
3
1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 2, 9, 4, 1, 0, 0, 0, 0, 1, 13, 20, 6, 1, 0, 0, 0, 0, 0, 11, 49, 40, 7, 1, 0, 0, 0, 0, 0, 5, 77, 158, 70, 9, 1, 0, 0, 0, 0, 0, 2, 75, 406, 426, 121, 11, 1, 0, 0, 0, 0, 0, 0, 47, 662, 1645, 1018, 189, 13, 1, 0
OFFSET
1,19
LINKS
Georg Grasegger, Table of n, a(n) for n = 1..351 (26 rows) (first 210 terms (20 rows) from Andrew Howroyd)
FORMULA
T(n, n) = 1 for n >= 3.
T(n, n-1) = A253186(n-3) for n >= 3.
EXAMPLE
Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
1;
0, 0;
0, 1, 0;
0, 0, 1, 0;
0, 0, 1, 1, 0;
0, 0, 1, 2, 1, 0;
0, 0, 0, 3, 3, 1, 0;
0, 0, 0, 2, 9, 4, 1, 0;
0, 0, 0, 1, 13, 20, 6, 1, 0;
0, 0, 0, 0, 11, 49, 40, 7, 1, 0;
0, 0, 0, 0, 5, 77, 158, 70, 9, 1, 0;
0, 0, 0, 0, 2, 75, 406, 426, 121, 11, 1, 0;
...
PROG
(nauty) geng -C $k $n:$n | planarg -q | countg -q # Georg Grasegger, Jun 05 2023
CROSSREFS
Row sums are A343869.
Column sums are A021103.
Cf. A049334, A049336 (transpose), A049337, A253186, A339070.
Sequence in context: A073797 A037856 A037874 * A339070 A352553 A077655
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 04 2021
STATUS
approved