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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.

%I A379430 #13 Jun 15 2025 16:55:09
%S A379430 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,
%T A379430 501,140,14,34,473,2264,4744,4744,2264,473,34,95,1670,10087,27768,
%U A379430 38495,27768,10087,1670,95,280,5969,44310,153668,279698,279698,153668,44310,5969,280
%N 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.
%C A379430 The planar maps considered are connected and may contain loops and parallel edges.
%C A379430 The number of edges is n + k - 2.
%H A379430 Timothy R. Walsh, <a href="/A007401/a007401.pdf">Number of sensed planar maps with n edges and m vertices</a>, pp. 1-10.
%F A379430 A(n,k) = A(k,n).
%e A379430 Array begins:
%e A379430 =========================================================
%e A379430 n\k |  1    2     3      4      5      6      7     8 ...
%e A379430 ----+----------------------------------------------------
%e A379430   1 |  1    1     1      2      3      6     14    34 ...
%e A379430   2 |  1    2     5     14     42    140    473  1670 ...
%e A379430   3 |  1    5    23    108    501   2264  10087 44310 ...
%e A379430   4 |  2   14   108    761   4744  27768 153668 ...
%e A379430   5 |  3   42   501   4744  38495 279698 ...
%e A379430   6 |  6  140  2264  27768 279698 ...
%e A379430   7 | 14  473 10087 153668 ...
%e A379430   8 | 34 1670 44310 ...
%e A379430    ...
%e A379430 As a triangle, rows give the number of edges (first row is 0 edges):
%e A379430    1;
%e A379430    1,    1;
%e A379430    1,    2,     1;
%e A379430    2,    5,     5,     2;
%e A379430    3,   14,    23,    14,     3;
%e A379430    6,   42,   108,   108,    42,     6;
%e A379430   14,  140,   501,   761,   501,   140,    14;
%e A379430   34,  473,  2264,  4744,  4744,  2264,   473,   34;
%e A379430   95, 1670, 10087, 27768, 38495, 27768, 10087, 1670, 95;
%e A379430   ...
%Y A379430 Antidiagonal sums are A006384.
%Y A379430 Columns 1..2 are A002995, A380237.
%Y A379430 Cf. A269920 (rooted), A277741 (unsensed), A379431 (achiral), A342061 (2-connected), A384964 (simple).
%K A379430 nonn,tabl
%O A379430 1,5
%A A379430 _Andrew Howroyd_, Jan 13 2025