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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 (list; graph; refs; listen; history; text; internal format)
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(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: 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

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Last modified June 25 04:15 EDT 2021. Contains 345452 sequences. (Running on oeis4.)