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A160844 Number of lines through at least 2 points of a 4 X n grid of points. 2
0, 1, 18, 35, 62, 93, 136, 181, 238, 299, 370, 445, 532, 621, 722, 827, 942, 1061, 1192, 1325, 1470, 1619, 1778, 1941, 2116, 2293, 2482, 2675, 2878, 3085, 3304, 3525, 3758, 3995, 4242, 4493, 4756, 5021, 5298, 5579, 5870, 6165, 6472, 6781, 7102, 7427, 7762 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

S. Mustonen, On lines and their intersection points in a rectangular grid of points

Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

FORMULA

a(n) = 2*a(n-1) - a(n-2) + C(mod(n+2,6) + 1)), C=(10,4,12,2,12,4).

From Colin Barker, May 24 2015: (Start)

  a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n > 5.

  G.f.: x*(4*x^6 - 3*x^4 + 9*x^3 + 16*x^2 + 17*x + 1) / ((1-x)^3*(x + 1)*(x^2 + x + 1)).

(End)

MATHEMATICA

a[0]=0; a[1]=1; a[2]=18; a[3]=35; a[n_]:=a[n]=a[n]=2*a[n-1]-a[n-2]+R[n] c4={10, 4, 12, 2, 12, 4}; R[n_]:=c4[[Mod[n+2, 6]+1]] Table[a[n], {n, 0, 46}]

Join[{0, 1}, LinearRecurrence[{1, 1, 0, -1, -1, 1}, {18, 35, 62, 93, 136, 181}, 50]] (* G. C. Greubel, Apr 30 2018 *)

PROG

(MAGMA) I:=[18, 35, 62, 93, 136, 181]; [0, 1] cat [n le 6 select I[n] else Self(n-1) +Self(n-2) -Self(n-4) -Self(n-5) +Self(n-6): n in [1..30]]; // G. C. Greubel, Apr 30 2018

(PARI) x='x+O('x^30); concat([0], Vec(x*(4*x^6-3*x^4+9*x^3+16*x^2+ 17*x+1 )/((1-x)^3*(x+1)*(x^2+x+1)))) \\ G. C. Greubel, Apr 30 2018

CROSSREFS

4th row/column of A107348, A295707.

Sequence in context: A014640 A245587 A215137 * A256878 A285318 A040306

Adjacent sequences:  A160841 A160842 A160843 * A160845 A160846 A160847

KEYWORD

nonn

AUTHOR

Seppo Mustonen, May 28 2009

STATUS

approved

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Last modified June 19 13:05 EDT 2021. Contains 345129 sequences. (Running on oeis4.)