login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A151890
Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
4
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
0,3
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
See A083487 for another version.
Sequence in context: A072009 A257502 A201207 * A356155 A227352 A255140
KEYWORD
nonn,tabl,easy
AUTHOR
N. J. A. Sloane, Jul 23 2009
EXTENSIONS
More terms from Alois P. Heinz, Oct 10 2009
STATUS
approved