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A123919
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Number of numbers congruent to 2 or 4 mod 6 and <= n.
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3
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0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 26
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OFFSET
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1,4
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COMMENTS
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a(n+2) is the graph radius of the n X n knight graph for n > 7. - Eric W. Weisstein, Nov 20 2019
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LINKS
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FORMULA
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a(n) = floor(n/2) - floor(n/6).
G.f.: x^2*(1+x^2)/((1+x)*(1-x)^2*(1+x+x^2)*(1-x+x^2)).
a(n+1) - a(n) = A120325(n+1). (End)
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 1, 2, 2, 2, 2}, 80] (* G. C. Greubel, Aug 07 2019 *)
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PROG
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(PARI) my(x='x+O('x^80)); concat([0], Vec(x^2*(1+x^2)/((1-x)*(1-x^6)))) \\ G. C. Greubel, Aug 07 2019
(PARI) a(n) = floor(n/2) - floor(n/6); \\ Joerg Arndt, Nov 23 2019
(GAP) a:=[0, 1, 1, 2, 2, 2, 2];; for n in [8..80] do a[n]:=a[n-1]+a[n-6]-a[n-7]; od; a; # G. C. Greubel, Aug 07 2019
(Magma) [Floor(n/2) - Floor(n/6) : n in [1..100]]; // Wesley Ivan Hurt, Apr 26 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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