login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 00:41 EST 2019. Contains 329816 sequences. (Running on oeis4.)