

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
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OFFSET

0,3


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
S. Mustonen, On lines and their intersection points in a rectangular grid of points
Index entries for linear recurrences with constant coefficients, signature (2,0,2,1).


FORMULA

a(n) = 2*n^2 + 3  n mod 2.
a(n) = 2*a(n1)  2*a(n3) + a(n4) for n > 5.  Colin Barker, May 24 2015
G.f.: x*(3*x^4  3*x^3  2*x^2 + 9*x + 1) / ((x1)^3*(x+1)).  Colin Barker, May 24 2015


MATHEMATICA

a[n_]:=If[n<2, n, 2*n^2+3Mod[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^43*x^32*x^2+9*x+1)/((x1)^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: A059407 A109376 A100038 * A153368 A068600 A158235
Adjacent sequences: A160840 A160841 A160842 * A160844 A160845 A160846


KEYWORD

nonn,easy


AUTHOR

Seppo Mustonen, May 28 2009


STATUS

approved



