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A187397 Number of distinct lines passing through 4 or more points in an n-by-n grid. 2
0, 0, 0, 10, 16, 22, 36, 54, 66, 92, 122, 156, 196, 240, 288, 366, 426, 490, 590, 698, 780, 904, 1036, 1176, 1326, 1484, 1650, 1874, 2060, 2254, 2512, 2782, 3006, 3300, 3606, 3924, 4256, 4600, 4956, 5398, 5782, 6178, 6666, 7170, 7608, 8144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..46.

FORMULA

Empirical g.f.: -2*x^4*(3*x^13 +2*x^12 +x^11 -6*x^10 -10*x^9 -6*x^8 +x^7 +7*x^6 +5*x^5 -x^4 -8*x^3 -11*x^2 -8*x -5) / ((x -1)^4*(x +1)^2*(x^2 +1)^2*(x^2 +x +1)^2). [Colin Barker, Feb 18 2013]

EXAMPLE

In the 4-by-4 grid, there are 4 horizontal lines, 4 vertical lines, and 2 main diagonals, for a total of 10.

CROSSREFS

Cf. A178465, A187062

Sequence in context: A083118 A136799 A055987 * A152138 A109100 A155151

Adjacent sequences:  A187394 A187395 A187396 * A187398 A187399 A187400

KEYWORD

nonn

AUTHOR

Sean A. Irvine, Mar 23 2011

STATUS

approved

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Last modified May 20 01:43 EDT 2013. Contains 225445 sequences.