A355553 Number of ways to select 3 or more collinear points from an n X n grid.

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, Table of n, a(n) for n = 1..71

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

Adjacent sequences: A355550 A355551 A355552 * A355554 A355555 A355556

Keyword

nonn

Author

Thomas Garrison, Jul 14 2022

Extensions

Corrected and extended by Lucas A. Brown, Nov 06 2022

Status

approved