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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.

%I A333278 #17 Mar 15 2020 17:10:27
%S A333278 8,28,92,80,296,872,178,652,1922,4344,372,1408,4256,9738,21284,654,
%T A333278 2470,7466,16978,36922,64172,1124,4312,13112,29874,64800,113494,
%U A333278 200028,1782,6774,20812,47402,103116,181484,319516,509584,2724,10428,31776,72398,158352,279070,490396,782096,1199428
%N 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.
%C A333278 T(n,m) = A288180(n,m)+A288187(n,m)-1 (Euler).
%C A333278 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 A333278 Hugo Pfoertner, <a href="/A288180/a288180_1.pdf">Illustration of intersection points up to 6 X 6</a>.
%e A333278 Triangle begins:
%e A333278 8,
%e A333278 28, 92,
%e A333278 80, 296, 872,
%e A333278 178, 652, 1922, 4344,
%e A333278 372, 1408, 4256, 9738, 21284,
%e A333278 654, 2470, 7466, 16978, 36922, 64172,
%e A333278 ...
%Y A333278 Cf. A288180.
%Y A333278 For column 1 see A331757. For column 2 see A333279, A333280, A333281.
%Y A333278 Cf. A331452, A288187; A331766, A331765, A331763; A333279, A333280, A333281.
%K A333278 nonn,tabl,more
%O A333278 1,1
%A A333278 _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 15 2020