A049337 - OEIS

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A049337

Triangle read by rows: T(n,k) is the number of 3-connected planar graphs (or polyhedra) with n >= 1 nodes and 0 <= k <= C(n,2) edges.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 11, 8, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 11, 42, 74, 76, 38, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 74, 296, 633, 768, 558, 219, 50

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

OFFSET

1,33

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..469; rows 1..14 flattened

EXAMPLE

Triangle begins

0,0;

0,0,0,0;

0,0,0,1,0,0,0;

0,0,0,0,0,1,1,0,0,0;

0,0,0,0,0,0,1,2,2,...;

...

From Hugo Pfoertner, Nov 24 2020: (Start)

Transposed table:

Nodes Sums

4 5 6 7 8 9 10 11 12 13 14 |A002840

Edges-+--+--+---+---+----+-----+------+------+-----+---+|-------

6 | 1 . . . . . . . . . . | 1

7 | . . . . . . . . . . . | 0

8 | . 1 . . . . . . . . . | 1

9 | . 1 1 . . . . . . . . | 2

10 | . . 2 . . . . . . . . | 2

11 | . . 2 2 . . . . . . . | 4

12 | . . 2 8 2 . . . . . . | 12

13 | . . . 11 11 . . . . . . | 22

14 | . . . 8 42 8 . . . . . | 58

15 | . . . 5 74 74 5 . . . . | 158

16 | . . . . 76 296 76 . . . . | 448

17 | . . . . 38 633 633 38 . . . | 1342

18 | . . . . 14 768 2635 768 14 . . | 4199

19 | . . . . . 538 6134 6134 558 . . | 13384

20 | . . . . . 219 8822 25626 8822 219 . | 43708

21 | . . . . . 50 7916 64439 64439 7916 50 | 144810

.. | . . . . . . .. .. .. .. .. | ..

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

Sums 1 2 7 34 257 2606 32300 440564 6384634 .. A000944

(End)

CROSSREFS

Cf. A000944, A002840, A021103, A003094, A049334.

A049337, A058787, A212438 are all versions of the same triangle.

Cf. A058788.

Sequence in context: A006831 A356816 A016414 * A049801 A076953 A180472

Adjacent sequences: A049334 A049335 A049336 * A049338 A049339 A049340

KEYWORD

nonn,tabf,nice

AUTHOR

Brendan McKay

EXTENSIONS

Missing zeros inserted by Sean A. Irvine, Jul 29 2021

STATUS

approved