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A060891 a(n) = n^6 - n^3 + 1.

%I A060891 #31 Dec 20 2024 10:12:43
%S A060891 1,1,57,703,4033,15501,46441,117307,261633,530713,999001,1770231,
%T A060891 2984257,4824613,7526793,11387251,16773121,24132657,34006393,47039023,
%U A060891 63992001,85756861,113369257,148023723,191089153,244125001,308898201,387400807,481868353,594798933,728973001
%N A060891 a(n) = n^6 - n^3 + 1.
%C A060891 a(n) = Phi_18(n) where Phi_k(x) is the k-th cyclotomic polynomial.
%H A060891 Harry J. Smith, <a href="/A060891/b060891.txt">Table of n, a(n) for n = 0..1000</a>
%H A060891 <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%H A060891 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A060891 G.f.: (1-6*x+71*x^2+290*x^3+309*x^4+52*x^5+3*x^6)/(1-x)^7. - _Colin Barker_, Apr 22 2012
%p A060891 with (combinat):seq(fibonacci(3,n^3)-n^3, n=0..30); # _Zerinvary Lajos_, May 25 2008
%p A060891 # Alternative
%p A060891 A060891 := proc(n)
%p A060891         numtheory[cyclotomic](18,n) ;
%p A060891 end proc:
%p A060891 seq(A060891(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014
%t A060891 Array[#^6 - #^3 + 1 &, 51, 0] (* or *)
%t A060891 Cyclotomic[18, Range[0, 50]] (* _Paolo Xausa_, Feb 26 2024 *)
%o A060891 (PARI) a(n) = { n^6 - n^3 + 1 } \\ _Harry J. Smith_, Jul 14 2009
%o A060891 (PARI) a(n) = polcyclo(18, n); \\ _Michel Marcus_, Dec 16 2017
%K A060891 nonn,easy
%O A060891 0,3
%A A060891 _N. J. A. Sloane_, May 05 2001