|
|
A331453
|
|
Triangle read by rows: T(n,m) (n >= m >= 1) = number of vertices formed by drawing the lines connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares.
|
|
13
|
|
|
5, 13, 37, 35, 99, 257, 75, 213, 421, 817, 159, 401, 881, 1489, 2757, 275, 657, 1305, 2143, 3555, 4825, 477, 1085, 2131, 3431, 5821, 7663, 12293, 755, 1619, 2941, 4817, 7477, 9913, 15037, 19241, 1163, 2327, 4369, 6495, 10393, 13647, 20425, 24651, 33549, 1659, 3257, 5603, 8637, 13689, 16953, 25125, 30779, 39857, 49577
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Take a grid of m+1 X n+1 points. There are 2*(m+n) points on the perimeter. Join every pair of the perimeter points by a line (of finite length). The lines do not extend outside the grid. T(m,n) is the number of vertices in the resulting diagram, and A331452(m,n) and A331454(m,n) give the number of regions and the number of line segments respectively.
For illustrations see the links in A331452.
|
|
LINKS
|
N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.
|
|
EXAMPLE
|
Triangle begins:
5,
13, 37,
35, 99, 257,
75, 213, 421, 817,
159, 401, 881, 1489, 2757,
275, 657, 1305, 2143, 3555, 4825,
477, 1085, 2131, 3431, 5821, 7663, 12293,
755, 1619, 2941, 4817, 7477, 9913, 15037, 19241,
1163, 2327, 4369, 6495, 10393, 13647, 20425, 24651, 33549,
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|