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%I #26 Feb 26 2024 14:31:39
%S 1,1,57,703,4033,15501,46441,117307,261633,530713,999001,1770231,
%T 2984257,4824613,7526793,11387251,16773121,24132657,34006393,47039023,
%U 63992001,85756861,113369257,148023723,191089153,244125001,308898201
%N a(n) = n^6 - n^3 + 1.
%C a(n) = Phi_18(n) where Phi_k(x) is the k-th cyclotomic polynomial.
%H Harry J. Smith, <a href="/A060891/b060891.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F 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 with (combinat):seq(fibonacci(3,n^3)-n^3, n=0..30); # _Zerinvary Lajos_, May 25 2008
%p # Alternative
%p A060891 := proc(n)
%p numtheory[cyclotomic](18,n) ;
%p end proc:
%p seq(A060891(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014
%t Array[#^6 - #^3 + 1 &, 51, 0] (* or *)
%t Cyclotomic[18, Range[0, 50]] (* _Paolo Xausa_, Feb 26 2024 *)
%o (PARI) { for (n=0, 1000, write("b060891.txt", n, " ", n^6 - n^3 + 1); ) } \\ _Harry J. Smith_, Jul 14 2009
%o (PARI) a(n) = polcyclo(18, n); \\ _Michel Marcus_, Dec 16 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 05 2001
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