

A151890


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


3



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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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
Adjacent sequences: A151887 A151888 A151889 * A151891 A151892 A151893


KEYWORD

nonn,tabl,easy


AUTHOR

N. J. A. Sloane, Jul 23 2009


EXTENSIONS

More terms from Alois P. Heinz, Oct 10 2009


STATUS

approved



