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A160843
Number of lines through at least 2 points of a 3 X n grid of points.
2
0, 1, 11, 20, 35, 52, 75, 100, 131, 164, 203, 244, 291, 340, 395, 452, 515, 580, 651, 724, 803, 884, 971, 1060, 1155, 1252, 1355, 1460, 1571, 1684, 1803, 1924, 2051, 2180, 2315, 2452, 2595, 2740, 2891, 3044, 3203, 3364, 3531, 3700, 3875, 4052, 4235, 4420
OFFSET
0,3
FORMULA
a(n) = 2*n^2 + 3 - n mod 2.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 5. - Colin Barker, May 24 2015
G.f.: -x*(3*x^4 - 3*x^3 - 2*x^2 + 9*x + 1) / ((x-1)^3*(x+1)). - Colin Barker, May 24 2015
MATHEMATICA
a[n_]:=If[n<2, n, 2*n^2+3-Mod[n, 2]] Table[a[n], {n, 0, 47}]
Join[{0, 1}, LinearRecurrence[{2, 0, -2, 1}, {11, 20, 35, 52}, 20]] (* G. C. Greubel, Apr 30 2018 *)
PROG
(PARI) Vec(-x*(3*x^4-3*x^3-2*x^2+9*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, May 24 2015
(Magma) [0, 1] cat [2*n^2 + 3 - n mod 2: n in [2..100]]; / G. C. Greubel, Apr 30 2018
CROSSREFS
3rd row/column of A107348, A295707.
Sequence in context: A109376 A100038 A370917 * A153368 A068600 A158235
KEYWORD
nonn,easy
AUTHOR
Seppo Mustonen, May 28 2009
STATUS
approved