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Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
4

%I #24 Jan 26 2020 21:29:55

%S 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 71,84,7,22,37,52,67,82,97,112,8,25,42,59,76,93,110,127,144,9,28,47,

%U 66,85,104,123,142,161,180,10,31,52,73,94,115,136,157,178,199,220,11,34,57

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

%C T(n,m) is also the edge count of the (n+1) X (m+1) grid graph. - _Eric W. Weisstein_, Jul 21 2011

%H Michael De Vlieger, <a href="/A151890/b151890.txt">Table of n, a(n) for n = 0..11475</a> (rows 0 <= n <= 150, flattened)

%F 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 Triangle begins:

%e 0;

%e 1, 4;

%e 2, 7, 12;

%e 3, 10, 17, 24;

%e 4, 13, 22, 31, 40;

%e 5, 16, 27, 38, 49, 60;

%e The 3 X 2 grid graph has 7 edges, which equals T(2,1).

%e The 4 X 4 grid graph has 24 edges, which equals T(3,3).

%p T:= (l, c)-> 2*l*c + l + c:

%p seq(seq(T(l, c), c=0..l), l=0..14); # _Alois P. Heinz_, Oct 10 2009

%t Table[2 m n + m + n, {n, 0, 9}, {m, 0, n}]

%Y See A083487 for another version.

%K nonn,tabl,easy

%O 0,3

%A _N. J. A. Sloane_, Jul 23 2009

%E More terms from _Alois P. Heinz_, Oct 10 2009