A378103 - OEIS

A378103

Triangle read by rows: T(n,k) is the number of n-node connected unsensed 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, 4, 4, 5, 4, 0, 0, 2, 6, 10, 14, 14, 18, 16, 0, 0, 0, 7, 18, 35, 49, 63, 69, 88, 78, 0, 0, 0, 5, 28, 74, 131, 204, 274, 345, 396, 489, 457, 0, 0, 0, 0, 26, 126, 304, 574, 893, 1290, 1708, 2137, 2503, 3071, 2938, 0, 0, 0, 0, 13, 159, 582, 1396, 2613, 4274, 6270, 8709, 11433, 14227, 16905, 20667, 20118

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

OFFSET

3,8

COMMENTS

The planar maps considered are without loops or isthmuses.

In other words, a(n) is the number of embeddings in the plane of connected bridgeless planar simple graphs with n vertices and k triangular internal faces.

The number of edges is n + k - 1.

The nonzero terms in row n range from k = floor(n/2) through 2*n-5 and, thus, the number of nonzero terms is 2n - floor(n/2) - 4 = A001651(n-2).

LINKS

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

Ya-Ping Lu, Illustration of initial terms

FORMULA

T(n, 2*n-5) = A002713(n-3).

T(n,k) = (A378336(n,k) + A378340(n,k))/2.

EXAMPLE

Triangle begins:

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

---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----

3 1

4 0 1 1

5 0 1 1 2 1

6 0 0 2 4 4 5 4

7 0 0 2 6 10 14 14 18 16

8 0 0 0 7 18 35 49 63 69 88 78

PROG

(PARI) my(A=A378103rows(10)); for(i=1, #A, print(A[i])) \\ See PARI link in A378340 for program code. - Andrew Howroyd, Nov 25 2024

CROSSREFS

Row sums are A377785.

Cf. A001651, A002713, A003094, A169808, A378336 (sensed), A378340 (achiral).

The final 3 terms of each row are in A002713, A005500, A005501.

Sequence in context: A059220 A261630 A301503 * A378336 A059431 A289358

Adjacent sequences: A378100 A378101 A378102 * A378104 A378105 A378106

KEYWORD

nonn,tabf

AUTHOR

Ya-Ping Lu, Nov 16 2024

EXTENSIONS

a(39) onwards from Andrew Howroyd, Nov 25 2024

STATUS

approved