OFFSET
0,2
COMMENTS
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
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
a(n) = A058794(n-2) for n>1. - Altug Alkan, May 03 2018
EXAMPLE
a(4) = 52 since (4 + i)^3 = (52 + 47i); where 47 = A080663(4).
MATHEMATICA
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 *)
PROG
(PARI) Vec(-2*x*(x^2-5*x+1)/(x-1)^4 + O(x^100)); \\ Colin Barker, Oct 16 2013
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Gary W. Adamson, Aug 14 2006
EXTENSIONS
Terms corrected, new name, and more terms from Colin Barker, Oct 16 2013
STATUS
approved