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A378340 Triangle read by rows: T(n,k) is the number of n node connected achiral planar maps with an external face and k triangular internal faces, n >= 3, 1 <= k <= 2*n - 5.

%I A378340 #15 Dec 16 2024 14:42:52
%S A378340 1,0,1,1,0,1,1,2,1,0,0,2,3,3,4,3,0,0,2,4,7,8,7,10,8,0,0,0,4,8,15,19,
%T A378340 22,19,29,23,0,0,0,3,11,22,32,48,57,65,57,86,68,0,0,0,0,8,25,47,82,
%U A378340 104,150,175,200,176,266,215,0,0,0,0,7,26,64,123,186,288,346,488,556,634,557,844,680
%N A378340 Triangle read by rows: T(n,k) is the number of n node connected achiral planar maps with an external face and k triangular internal faces, n >= 3, 1 <= k <= 2*n - 5.
%C A378340 See A378103 for illustration of initial terms. This sequence counts only those maps which have mirror symmetry.
%C A378340 The planar maps considered are without loops or isthmuses.
%C A378340 The number of edges is n + k - 1.
%H A378340 Andrew Howroyd, <a href="/A378340/b378340.txt">Table of n, a(n) for n = 3..2306</a> (rows 3..50)
%H A378340 Andrew Howroyd, <a href="/A378340/a378340.txt">PARI Program</a>, Nov 2024.
%F A378340 T(n,2*n-5) = A002712(n-3). - _Ya-Ping Lu_, Dec 16 2024
%e A378340 Triangle begins:
%e A378340 n\k | 1  2  3  4   5   6   7   8   9  10  11  12  13
%e A378340 ----+------------------------------------------------
%e A378340   3 | 1;
%e A378340   4 | 0, 1, 1;
%e A378340   5 | 0, 1, 1, 2,  1;
%e A378340   6 | 0, 0, 2, 3,  3,  4,  3;
%e A378340   7 | 0, 0, 2, 4,  7,  8,  7, 10,  8;
%e A378340   8 | 0, 0, 0, 4,  8, 15, 19, 22, 19, 29, 23;
%e A378340   9 | 0, 0, 0, 3, 11, 22, 32, 48, 57, 65, 57, 86, 68;
%e A378340   ...
%o A378340 (PARI) my(A=A378340rows(10)); for(i=1, #A, print(A[i])) \\ See Links for program.
%Y A378340 Row sums are A378339.
%Y A378340 Column sums are A378341.
%Y A378340 Antidiagonal sums are A378342.
%Y A378340 Cf. A378103 (unsensed), A378336 (sensed), A002712.
%K A378340 nonn,tabf
%O A378340 3,8
%A A378340 _Andrew Howroyd_, Nov 25 2024