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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
OFFSET
1,2
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-François Alcover, Sep 03 2018 *)
CROSSREFS
Row 5 of A271910.
Sequence in context: A100150 A305950 A060334 * A187163 A211577 A101862
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 24 2016
STATUS
approved