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A102309
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a(n) = Sum_{d divides n} moebius(d) * C(n/d,2).
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8
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0, 0, 1, 3, 5, 10, 11, 21, 22, 33, 34, 55, 46, 78, 69, 92, 92, 136, 105, 171, 140, 186, 175, 253, 188, 290, 246, 315, 282, 406, 284, 465, 376, 470, 424, 564, 426, 666, 531, 660, 568, 820, 570, 903, 710, 852, 781, 1081, 760, 1155, 890, 1136, 996, 1378, 963, 1420, 1140, 1422, 1246
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OFFSET
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0,4
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COMMENTS
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Apparently, a(n-1) is the number of periodic complex Horadam orbits with period n, for n>2. - Nathaniel Johnston, Oct 04 2013
Also apparently, the first differences of A100448 (checked up to n=2000).
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} mu(k) * x^(2*k)/(1 - x^k)^3. - Seiichi Manyama, May 24 2021
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MAPLE
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with(numtheory):
a:= n-> add(mobius(d)*binomial(n/d, 2), d=divisors(n)):
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MATHEMATICA
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a[n_] := Sum[MoebiusMu[d] Binomial[n/d, 2], {d, Divisors[n]}];
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(d) * binomial(n/d, 2) ); /* Joerg Arndt, Feb 18 2013 */
(PARI) my(N=66, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, moebius(k)*x^(2*k)/(1-x^k)^3))) \\ Seiichi Manyama, May 24 2021
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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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