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A225948
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a(0) = -1; for n>0, a(n) = numerator(1/4 - 4/n^2).
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7
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-1, -15, -3, -7, 0, 9, 5, 33, 3, 65, 21, 105, 2, 153, 45, 209, 15, 273, 77, 345, 6, 425, 117, 513, 35, 609, 165, 713, 12, 825, 221, 945, 63, 1073, 285, 1209, 20, 1353, 357, 1505, 99, 1665, 437, 1833, 30, 2009, 525, 2193, 143
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OFFSET
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0,2
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COMMENTS
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Fractions in lowest terms for n>0: -15/4, -3/4, -7/36, 0/1, 9/100, 5/36, 33/196, 3/16, 65/324, 21/100, 105/484, 2/9, 153/676, 45/196, 209/900, 15/64,...
If t(n) is the sequence with period 8: 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, ... (see A226044), then A226008(n) = 4*a(n) + t(n).
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LINKS
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FORMULA
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a(n) = 3*a(n-8) -3*a(n-16) +a(n-24).
G.f.: -(1 +15*x +3*x^2 +7*x^3 -9*x^5 -5*x^6 -33*x^7 -6*x^8 -110*x^9 -30*x^10 -126*x^11 -2*x^12 -126*x^13 -30*x^14 -110*x^15 -3*x^16 -33*x^17 -5*x^18 -9*x^19 +7*x^21 +3*x^22 +15*x^23)/(1-x^8)^3. - Bruno Berselli, May 22 2013
a(n) = (n^2-16)*(6*cos(Pi*n/4)-54*cos(Pi*n/2)+6*cos(3*Pi*n/4)-219*(-1)^n+293)/512. - Bruno Berselli, May 22 2013
a(n+10) = a(n+2)*(n+14)/(n-2) for n=0,1 and n>2. - Bruno Berselli, May 22 2013
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MATHEMATICA
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Join[{-1}, Table[Numerator[1/4 - 4/n^2], {n, 50}]] (* Bruno Berselli, May 24 2013 *)
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PROG
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(Magma) [-1] cat [Numerator(1/4-4/n^2): n in [1..50]]; // Bruno Berselli, May 22 2013
(PARI) concat([-1], vector(100, n, numerator(1/4 - 4/n^2))) \\ G. C. Greubel, Sep 19 2018
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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