OFFSET
0,3
COMMENTS
T(n,m) is also the edge count of the (n+1) X (m+1) grid graph. - Eric W. Weisstein, Jul 21 2011
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened)
FORMULA
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
EXAMPLE
Triangle begins:
0;
1, 4;
2, 7, 12;
3, 10, 17, 24;
4, 13, 22, 31, 40;
5, 16, 27, 38, 49, 60;
The 3 X 2 grid graph has 7 edges, which equals T(2,1).
The 4 X 4 grid graph has 24 edges, which equals T(3,3).
MAPLE
T:= (l, c)-> 2*l*c + l + c:
seq(seq(T(l, c), c=0..l), l=0..14); # Alois P. Heinz, Oct 10 2009
MATHEMATICA
Table[2 m n + m + n, {n, 0, 9}, {m, 0, n}]
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jul 23 2009
EXTENSIONS
More terms from Alois P. Heinz, Oct 10 2009
STATUS
approved