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A271915 Number of ways to choose three distinct points from a 5 X n grid so that they form an isosceles triangle. 4
0, 24, 108, 248, 444, 672, 932, 1204, 1512, 1836, 2188, 2548, 2936, 3332, 3756, 4192, 4656, 5128, 5628, 6136, 6672, 7216, 7788, 8368, 8976, 9592, 10236, 10888, 11568, 12256, 12972, 13696, 14448, 15208, 15996, 16792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..36.

Chai Wah Wu, Counting the number of isosceles triangles in rectangular regular grids, arXiv:1605.00180 [math.CO], 2016.

FORMULA

Conjectured g.f.: 4*x* (x^16-x^14+2*x^10+2*x^9-x^8-x^7 + 5*x^6+6*x^5+6*x^4+x^3-8*x^2-15*x-6) /((x+1)*(x-1)^3).

Conjectured recurrence: a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n > 18.

The conjectured g.f. and recurrence are true. See paper in links. - Chai Wah Wu, May 07 2016

MATHEMATICA

Join[{0, 24, 108, 248, 444, 672, 932, 1204, 1512, 1836, 2188, 2548, 2936, 3332}, LinearRecurrence[{2, 0, -2, 1}, {3756, 4192, 4656, 5128}, 20]] (* Jean-Fran├žois Alcover, Sep 03 2018 *)

CROSSREFS

Row 5 of A271910.

Cf. A186434, A187452.

Sequence in context: A100150 A305950 A060334 * A187163 A211577 A101862

Adjacent sequences:  A271912 A271913 A271914 * A271916 A271917 A271918

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 24 2016

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)