A333278 Triangle read by rows: T(n,m) (n >= m >= 1) = number of edges in the graph formed by drawing the line segments connecting any two of the (n+1) X (m+1) lattice points in an n X m grid of squares.

8, 28, 92, 80, 296, 872, 178, 652, 1922, 4344, 372, 1408, 4256, 9738, 21284, 654, 2470, 7466, 16978, 36922, 64172, 1124, 4312, 13112, 29874, 64800, 113494, 200028, 1782, 6774, 20812, 47402, 103116, 181484, 319516, 509584, 2724, 10428, 31776, 72398, 158352, 279070, 490396, 782096, 1199428

Offset

1,1

Comments

T(n,m) = A288180(n,m)+A288187(n,m)-1 (Euler).

For the graphs defined in A331452 and A288187 only the counts for graphs that are one square wide have formulas for regions, edges, and vertices (see A306302, A331757, A331755). For width 2 there are six such sequences (A331766, A331765, A331763; A333279, A333280, A333281). It would be nice to have a formula for any one of them.

Links

Table of n, a(n) for n=1..45.

Hugo Pfoertner, Illustration of intersection points up to 6 X 6.

Example

Triangle begins:
8,
28, 92,
80, 296, 872,
178, 652, 1922, 4344,
372, 1408, 4256, 9738, 21284,
654, 2470, 7466, 16978, 36922, 64172,
...

Crossrefs

Cf. A288180.

For column 1 see A331757. For column 2 see A333279, A333280, A333281.

Cf. A331452, A288187; A331766, A331765, A331763; A333279, A333280, A333281.

Sequence in context: A200941 A332600 A331454 * A333283 A211066 A095857

Adjacent sequences: A333275 A333276 A333277 * A333279 A333280 A333281

Keyword

nonn,tabl,more

Author

Scott R. Shannon and N. J. A. Sloane, Mar 15 2020

Status

approved