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A271913
Number of ways to choose three distinct points from a 4 X n grid so that they form an isosceles triangle.
4
0, 16, 68, 148, 248, 360, 488, 620, 768, 924, 1096, 1272, 1464, 1660, 1872, 2088, 2320, 2556, 2808, 3064, 3336, 3612, 3904, 4200, 4512, 4828, 5160, 5496, 5848, 6204, 6576, 6952, 7344, 7740, 8152, 8568, 9000, 9436, 9888, 10344, 10816, 11292, 11784, 12280, 12792, 13308, 13840, 14376, 14928, 15484
OFFSET
1,2
FORMULA
Conjectured g.f.: 4*x*(x^10-x^8+2*x^6+x^5+4*x^4+4*x^3-3*x^2-9*x-4)/((x+1)*(x-1)^3).
Conjectured recurrence: a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n > 12.
Conjectures from Colin Barker, Apr 25 2016: (Start)
a(n) = -3/2*(143+(-1)^n)+64*n+5*n^2 for n>8.
a(n) = 5*n^2+64*n-216 for n>8 and even.
a(n) = 5*n^2+64*n-213 for n>8 and odd.
(End)
The conjectured g.f. and recurrence are true. See paper in links. - Chai Wah Wu, May 07 2016
MATHEMATICA
Join[{0, 16, 68, 148, 248, 360, 488, 620}, LinearRecurrence[{2, 0, -2, 1}, {768, 924, 1096, 1272}, 42]] (* Jean-François Alcover, Sep 03 2018 *)
CROSSREFS
Row 4 of A271910.
Sequence in context: A321180 A100186 A344600 * A178574 A005906 A247663
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 24 2016
EXTENSIONS
More terms from Jean-François Alcover, Sep 03 2018
STATUS
approved