A333278 - OEIS

%I #17 Mar 15 2020 17:10:27

%S 8,28,92,80,296,872,178,652,1922,4344,372,1408,4256,9738,21284,654,

%T 2470,7466,16978,36922,64172,1124,4312,13112,29874,64800,113494,

%U 200028,1782,6774,20812,47402,103116,181484,319516,509584,2724,10428,31776,72398,158352,279070,490396,782096,1199428

%N 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.

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

%C 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.

%H Hugo Pfoertner, <a href="/A288180/a288180_1.pdf">Illustration of intersection points up to 6 X 6</a>.

%e Triangle begins:

%e 8,

%e 28, 92,

%e 80, 296, 872,

%e 178, 652, 1922, 4344,

%e 372, 1408, 4256, 9738, 21284,

%e 654, 2470, 7466, 16978, 36922, 64172,

%e ...

%Y Cf. A288180.

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

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

%K nonn,tabl,more

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 15 2020