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A121670
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a(n) = n^3 - 3*n.
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9
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0, -2, 2, 18, 52, 110, 198, 322, 488, 702, 970, 1298, 1692, 2158, 2702, 3330, 4048, 4862, 5778, 6802, 7940, 9198, 10582, 12098, 13752, 15550, 17498, 19602, 21868, 24302, 26910, 29698, 32672, 35838, 39202, 42770, 46548, 50542, 54758, 59202, 63880, 68798, 73962
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OFFSET
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0,2
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COMMENTS
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Previous name was: Real part of (n + i)^3, companion to A080663.
Reversing the order of terms in (n + i)^3 to (1 + ni)^3 generates the terms of A080663. E.g, A080663(4) = 47 since (1 + 4i)^3 = (-47 - 52i). Or, (n + i)^3 = (a(n) + A080663(a)i) and (1 + ni)^3 = (-A080663(n) - a(n)i).
Also, numbers n such that the polynomial x^6 - n*x^3 + 1 is reducible. - Ralf Stephan, Oct 24 2013
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LINKS
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FORMULA
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a(n) = Re( (n + i)^3 ).
a(n) = n^3-3*n. a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: -2*x*(x^2-5*x+1) / (x-1)^4. - Colin Barker, Oct 16 2013
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EXAMPLE
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a(4) = 52 since (4 + i)^3 = (52 + 47i); where 47 = A080663(4).
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MATHEMATICA
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CoefficientList[Series[-2 x (x^2 - 5 x + 1)/(x - 1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 11 2014 *)
Table[n^3-3n, {n, 0, 60}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, -2, 2, 18}, 60] (* Harvey P. Dale, Nov 30 2021 *)
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PROG
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(PARI) Vec(-2*x*(x^2-5*x+1)/(x-1)^4 + O(x^100)); \\ Colin Barker, Oct 16 2013
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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Terms corrected, new name, and more terms from Colin Barker, Oct 16 2013
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STATUS
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approved
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