A058787 Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n faces and k vertices, where (n/2+2) <= k <= (2n+8).

1, 1, 1, 1, 2, 2, 2, 2, 8, 11, 8, 5, 2, 11, 42, 74, 76, 38, 14, 8, 74, 296, 633, 768, 558, 219, 50, 5, 76, 633, 2635, 6134, 8822, 7916, 4442, 1404, 233, 38, 768, 6134, 25626, 64439, 104213, 112082, 79773, 36528, 9714, 1249, 14, 558, 8822, 64439, 268394, 709302

Offset

4,5

Comments

Rows are of lengths 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, ... floor(3n/2)-5. See A001651 (this is the sequence of integers not divisible by 3).

Links

Table of n, a(n) for n=4..57.

G. P. Michon, Counting Polyhedra

Example

The irregular triangle T(n,k) begins:
  n\k: 4  5  6   7   8    9    10    11    12    13    14    15   16
  4:   1;
  5:      1, 1;
  6:      1, 2,  2,  2;
  7:         2,  8, 11,   8,    5;
  8:         2, 11, 42,  74,   76,   38,   14;
  9:             8, 74, 296,  633,  768,  558,  219,   50;
 10:             5, 76, 633, 2635, 6134, 8822, 7916, 4442, 1404, 233;
 ...
There are 38 polyhedra with 9 faces and 11 vertices, or with 11 faces and 9 vertices.

Crossrefs

Row sums are A000944.

Last entry in each row is A000109, also first entry in even rows.

Second-last entry in each row is A058786, also first entry in odd rows.

Cf. A001651 (length of rows), A002856, A002840.

A049337, A058787, A058788, A212438 are all versions of the same triangle.

Sequence in context: A152660 A392615 A339163 * A353392 A360310 A085056

Adjacent sequences: A058784 A058785 A058786 * A058788 A058789 A058790

Keyword

hard,nice,nonn,tabf

Author

Gerard P. Michon, Nov 29 2000

Status

approved