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

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, 71, 84, 7, 22, 37, 52, 67, 82, 97, 112, 8, 25, 42, 59, 76, 93, 110, 127, 144, 9, 28, 47, 66, 85, 104, 123, 142, 161, 180, 10, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220, 11, 34, 57

Offset: 0

Author

N. J. A. Sloane, Jul 23 2009

Keywords

• nonn
• tabl
• easy

Comments

T(n,m) is also the edge count of the (n+1) X (m+1) grid graph. - Eric W. Weisstein, Jul 21 2011

Examples

			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).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened)

Crossrefs

See A083487 for another version.

Programs

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}]

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

Extensions

More terms from Alois P. Heinz, Oct 10 2009