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%I #30 Sep 08 2022 08:45:03
%S 1,13,8191,797161,22369621,305175781,2612138803,16148168401,
%T 78536544841,317733228541,1111111111111,3452271214393,9726655034461,
%U 25239592216021,61054982558011,139013933454241,300239975158033,619036127056621
%N a(n) = Sum_{j=0..12} n^j.
%C a(n) = Phi_13(n) where Let Phi_k is the k-th cyclotomic polynomial.
%H Harry J. Smith, <a href="/A060887/b060887.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_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 a(n) = n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
%F G.f.: (x^12 + 2718*x^11 + 363156*x^10 + 8452952*x^9 + 59276439*x^8 + 155812164*x^7 + 167537592*x^6 + 74214648*x^5 + 12642423*x^4 + 691406*x^3 + 8100*x^2 + 1)/(1-x)^13. - _Colin Barker_, Oct 29 2012
%F a(n) = (n^13-1)/(n-1) with a(1) = 13 = lim_{x->1} a(x). - _M. F. Hasler_, Dec 31 2012
%p A060887 := proc(n)
%p numtheory[cyclotomic](13,n) ;
%p end proc:
%p seq(A060887(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014
%t Table[1 + Sum[n^j, {j, 1, 12}], {n, 0, 20}] (* _G. C. Greubel_, Apr 14 2019 *)
%o (PARI) { for (n=0, 1000, write("b060887.txt", n, " ", n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1); ) } \\ _Harry J. Smith_, Jul 14 2009
%o (PARI) A060887(n)=polcyclo(13,n) \\ _M. F. Hasler_, Dec 31 2012
%o (Magma) [(&+[n^j: j in [0..12]]): n in [0..20]]; // _G. C. Greubel_, Apr 14 2019
%o (Sage) [sum(n^j for j in (0..12)) for n in (0..20)] # _G. C. Greubel_, Apr 14 2019
%Y Cf. A053698, A053699, A053700, A053716, A053717, A102909, A103623, A060885, A102909, A104376, A104682, A105067.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 05 2001
%E Name changed by _G. C. Greubel_, Apr 14 2019
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