

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
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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
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(n1)  3*a(n2) + a(n3) for n > 4.  Colin Barker, May 24 2015
G.f.: x*(2*x^3  4*x^2 + 3*x + 1) / (x1)^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^34*x^2+3*x+1) / (x1)^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



