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A151890 Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).

%I A151890 #24 Jan 26 2020 21:29:55
%S A151890 0,1,4,2,7,12,3,10,17,24,4,13,22,31,40,5,16,27,38,49,60,6,19,32,45,58,
%T A151890 71,84,7,22,37,52,67,82,97,112,8,25,42,59,76,93,110,127,144,9,28,47,
%U A151890 66,85,104,123,142,161,180,10,31,52,73,94,115,136,157,178,199,220,11,34,57
%N A151890 Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
%C A151890 T(n,m) is also the edge count of the (n+1) X (m+1) grid graph. - _Eric W. Weisstein_, Jul 21 2011
%H A151890 Michael De Vlieger, <a href="/A151890/b151890.txt">Table of n, a(n) for n = 0..11475</a> (rows 0 <= n <= 150, flattened)
%F A151890 a(n) = -t^3 + (3/2)*t^2 + (2*n+1/2)*t - n - 1, where t = floor(sqrt(2n+1)+1/2) = round(sqrt(2n+1)). - _Ridouane Oudra_, Dec 02 2019
%e A151890 Triangle begins:
%e A151890   0;
%e A151890   1,  4;
%e A151890   2,  7, 12;
%e A151890   3, 10, 17, 24;
%e A151890   4, 13, 22, 31, 40;
%e A151890   5, 16, 27, 38, 49, 60;
%e A151890 The 3 X 2 grid graph has 7 edges, which equals T(2,1).
%e A151890 The 4 X 4 grid graph has 24 edges, which equals T(3,3).
%p A151890 T:= (l, c)-> 2*l*c + l + c:
%p A151890 seq(seq(T(l, c), c=0..l), l=0..14);  # _Alois P. Heinz_, Oct 10 2009
%t A151890 Table[2 m n + m + n, {n, 0, 9}, {m, 0, n}]
%Y A151890 See A083487 for another version.
%K A151890 nonn,tabl,easy
%O A151890 0,3
%A A151890 _N. J. A. Sloane_, Jul 23 2009
%E A151890 More terms from _Alois P. Heinz_, Oct 10 2009