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A160842 Number of lines through at least 2 points of a 2 X n grid of points. 4
0, 1, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403, 2502 (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

Seppo Mustonen, On lines and their intersection points in a rectangular grid of points [Local copy]

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = n^2 + 2 = A059100(n) for n > 1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. - Colin Barker, May 24 2015

G.f.: -x*(2*x^3 - 4*x^2 + 3*x + 1) / (x-1)^3. - Colin Barker, May 24 2015

Sum_{n>=1} 1/a(n) = Pi * coth(sqrt(2)*Pi) / 2^(3/2) - 1/4. - Vaclav Kotesovec, May 01 2018

MATHEMATICA

a[n_]:=If[n<2, n, n^2+2] Table[a[n], {n, 0, 50}]

Join[{0, 1}, Range[2, 50]^2+2] (* Harvey P. Dale, Feb 06 2015 *)

PROG

(PARI) Vec(-x*(2*x^3-4*x^2+3*x+1) / (x-1)^3 + O(x^100)) \\ Colin Barker, May 24 2015

(MAGMA) [0, 1] cat [n^2 + 2: n in [2..100]]; // G. C. Greubel, Apr 30 2018

CROSSREFS

Cf. A295707, A107348.

Sequence in context: A073945 A083500 A102305 * A007745 A188556 A021011

Adjacent sequences:  A160839 A160840 A160841 * A160843 A160844 A160845

KEYWORD

nonn,easy

AUTHOR

Seppo Mustonen, May 28 2009

STATUS

approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)