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%I #26 Aug 19 2016 00:39:48
%S 1,1,4033,530713,16773121,244125001,2176735681,13841169553,
%T 68719214593,282429005041,999999000001,3138426605161,8916097462273,
%U 23298080295673,56693904845761,129746326500001,281474959933441,582622213092193
%N n^12 - n^6 + 1.
%C a(n) = Phi_36(n) where Phi_k is the k-th cyclotomic polynomial.
%H Harry J. Smith, <a href="/A060896/b060896.txt">Table of n, a(n) for n = 0..1000</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: -(x^12 +4020*x^11 +478362*x^10 +10188140*x^9 +66317319*x^8 +162512496*x^7 +162514212*x^6 +66316032*x^5 +10188855*x^4 +478076*x^3 +4098*x^2 -12*x +1)/(x -1)^13. [_Colin Barker_, Oct 29 2012]
%F a(0)=1, a(1)=1, a(2)=4033, a(3)=530713, a(4)=16773121, a(5)=244125001, a(6)=2176735681, a(7)=13841169553, a(8)=68719214593, a(9)=282429005041, a(10)=999999000001, a(11)=3138426605161, a(12)=8916097462273, a(n)=13*a(n-1)- 78*a(n-2)+ 286*a(n-3)- 715*a(n-4)+ 1287*a(n-5)- 1716*a(n-6)+ 1716*a(n-7)- 1287*a(n-8)+ 715*a(n-9)- 286*a(n-10)+ 78*a(n-11)- 13*a(n-12)+ a(n-13). - _Harvey P. Dale_, Dec 16 2013
%p A060896 := proc(n)
%p numtheory[cyclotomic](36,n) ;
%p end proc:
%p seq(A060896(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014
%t Table[n^12-n^6+1,{n,0,30}] (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{1,1,4033,530713,16773121,244125001,2176735681,13841169553,68719214593,282429005041,999999000001,3138426605161,8916097462273},30] (* _Harvey P. Dale_, Dec 16 2013 *)
%o (PARI) { for (n=0, 1000, write("b060896.txt", n, " ", n^12 - n^6 + 1); ) } \\ _Harry J. Smith_, Jul 19 2009
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 05 2001
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