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A355553
Number of ways to select 3 or more collinear points from an n X n grid.
3
0, 0, 8, 54, 228, 708, 1980, 4890, 11528, 26004, 57384, 123786, 265596, 563664, 1192220, 2511474, 5279208, 11064216, 23156448, 48361110, 100859180, 209996772, 436635396, 906562842, 1879950384, 3893566872, 8054935784, 16645591974, 34363631412, 70872295524, 146036933100
OFFSET
1,3
LINKS
Lucas A. Brown, A355553.py.
EXAMPLE
a(4)=54: There are 4 horizontal lines of length 4 and within a line of 4 dots are 5 ways to select a line 3 or longer. There are 2 diagonal lines of length 4 and 4 vertical lines of length 4. Finally there are 4 diagonals of length 3 these are: ((1,2),(2,3),(3,4)),((2,1),(3,2),(4,3)),((1,3),(2,2),(3,1)),((2,4),(3,3),(4,2). In total we have 5*10+4=54.
4 . . . .
3 . . . .
2 . . . .
1 . . . .
1 2 3 4
CROSSREFS
Cf. A000982 (1 X n), 2*A000982 (2 X n), A355551 (3 X n), A355552 (4 X n).
Sequence in context: A085537 A085540 A259546 * A122657 A152692 A351845
KEYWORD
nonn
AUTHOR
Thomas Garrison, Jul 14 2022
EXTENSIONS
Corrected and extended by Lucas A. Brown, Nov 06 2022
STATUS
approved