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A338043
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Draw n rays from each of two distinct points in the plane; a(n) is the number of edges thus created. See Comments for details.
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3
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2, 3, 10, 7, 22, 15, 38, 27, 58, 43, 82, 63, 110, 87, 142, 115, 178, 147, 218, 183, 262, 223, 310, 267, 362, 315, 418, 367, 478, 423, 542, 483, 610, 547, 682, 615, 758, 687, 838, 763, 922, 843, 1010, 927, 1102, 1015, 1198, 1107, 1298, 1203, 1402, 1303, 1510, 1407
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OFFSET
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1,1
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COMMENTS
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The rays are evenly spaced around each point. The first ray of one point goes in the opposite direction of the other point. Should a ray hit the other point, it terminates there, i.e., it is converted to a line segment.
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LINKS
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FORMULA
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a(n) = (n^2 + 4*n - 1)/2, n odd; (n^2 - 2*n + 6)/2, n even (conjectured).
G.f.: x*(2 + x + 3*x^2 - 5*x^3 + 3*x^4)/((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5. (End)
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EXAMPLE
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For n=1: <-----x x-----> so a(1)=2.
For n=2: <-----x<--->x-----> so a(2)=3.
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PROG
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(PARI) a(n)=if(n%2==1, (n^2 + 4*n - 1)/2, (n^2 - 2*n + 6)/2)
vector(200, n, a(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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