|
| |
|
|
A119437
|
|
Table T(n,k) = number of lines through exactly k points of an n X n grid of points.
|
|
1
| |
|
|
6, 12, 8, 48, 4, 10, 108, 16, 4, 12, 248, 36, 4, 4, 14, 428, 64, 20, 4, 4, 16, 764, 100, 44, 4, 4, 4, 18, 1196, 204, 36, 24, 4, 4, 4, 20, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 2668, 396, 124, 40, 28, 4, 4, 4, 4, 24, 3824, 572, 200, 20, 60, 4, 4, 4, 4, 4, 26, 5244, 780, 236, 76, 44, 32
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
LINKS
| S. Mustonen, On lines and their intersection points in a rectangular grid of points [From Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 18 2009]
|
|
|
FORMULA
| T(n,k) = 1/2 (f(n, k+1) - 2 f(n, k) + f(n, k-1)) where f(n, k) = Sum_{-n<kx<n, -n<ky<n, gcd(x, y)=1} (n - |kx|)*(n - |ky|). [From Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 18 2009]
|
|
|
CROSSREFS
| Row sums A018808; columns A018809-A018817. See A119439 for another version.
Sequence in context: A028627 A162522 A028320 * A074474 A164378 A124349
Adjacent sequences: A119434 A119435 A119436 * A119438 A119439 A119440
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 19 2006
|
|
|
EXTENSIONS
| An incorrect formula removed by S. Mustonen (seppo.mustonen(AT)helsinki.fi), Apr 25 2009
|
| |
|
|
