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A142705
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Numerator of 1/4 - 1/(2n)^2.
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8
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0, 3, 2, 15, 6, 35, 12, 63, 20, 99, 30, 143, 42, 195, 56, 255, 72, 323, 90, 399, 110, 483, 132, 575, 156, 675, 182, 783, 210, 899, 240, 1023, 272, 1155, 306, 1295, 342, 1443, 380, 1599, 420, 1763, 462, 1935, 506, 2115, 552, 2303, 600, 2499, 650, 2703, 702
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OFFSET
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1,2
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COMMENTS
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Read modulo 10 (the last digits), a sequence with period length 10 results: 0, 3, 2, 5, 6, 5, 2, 3, 0, 9. Read modulo 9, a sequence with period length 18 results.
a(n) is the numerator of (n-1)*(n+1)/4. - Altug Alkan, Apr 19 2018
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LINKS
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FORMULA
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a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
G.f.: x^2*(3+2x+6x^2-x^4)/(1-x^2)^3. - R. J. Mathar, Oct 24 2008
E.g.f.: 1 + (1/4)*((4*x^2 + x - 4)*cosh(x) + (x^2 + 4*x -1)*sinh(x)). - G. C. Greubel, Jul 20 2017
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MATHEMATICA
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Numerator[Table[(1/4)*(1 - 1/n^2), {n, 1, 50}]] (* G. C. Greubel, Jul 20 2017 *)
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PROG
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(Magma) [-(3/4)*(-1)^n*n-(3/8)*(-1)^n*n^2+(5/8)*n^2+(5/4)*n: n in [0..60]]; // Vincenzo Librandi, Jul 02 2011
(PARI) for(n=1, 50, print1(numerator((1/4)*(1 - 1/n^2)), ", ")) \\ G. C. Greubel, Jul 20 2017
(PARI) a(n) = if(n%2, (n^2-1)/4, n^2-1); \\ Altug Alkan, Apr 19 2018
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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