A378340 - OEIS

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.

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, 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, 104, 150, 175, 200, 176, 266, 215, 0, 0, 0, 0, 7, 26, 64, 123, 186, 288, 346, 488, 556, 634, 557, 844, 680

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,8

COMMENTS

See A378103 for illustration of initial terms. This sequence counts only those maps which have mirror symmetry.

The planar maps considered are without loops or isthmuses.

The number of edges is n + k - 1.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..2306 (rows 3..50)

Andrew Howroyd, PARI Program, Nov 2024.

EXAMPLE

Triangle begins:

n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13

----+------------------------------------------------

3 | 1;

4 | 0, 1, 1;

5 | 0, 1, 1, 2, 1;

6 | 0, 0, 2, 3, 3, 4, 3;

7 | 0, 0, 2, 4, 7, 8, 7, 10, 8;

8 | 0, 0, 0, 4, 8, 15, 19, 22, 19, 29, 23;

9 | 0, 0, 0, 3, 11, 22, 32, 48, 57, 65, 57, 86, 68;

...

PROG

(PARI) my(A=A378340rows(10)); for(i=1, #A, print(A[i])) \\ See Links for program.

CROSSREFS

Row sums are A378339.

Column sums are A378341.

Antidiagonal sums are A378342.

Cf. A378103 (unsensed), A378336 (sensed).

Sequence in context: A275345 A259668 A261118 * A063181 A247310 A059220

Adjacent sequences: A378337 A378338 A378339 * A378341 A378342 A378343

KEYWORD

nonn,tabf,new

AUTHOR

Andrew Howroyd, Nov 25 2024

STATUS

approved