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A060893 n^8 - n^4 + 1. 2

%I

%S 1,1,241,6481,65281,390001,1678321,5762401,16773121,43040161,99990001,

%T 214344241,429960961,815702161,1475750641,2562840001,4294901761,

%U 6975673921,11019855601,16983432721,25599840001,37822664881,54875639281,78310705441,110074982401

%N n^8 - n^4 + 1.

%C a(n) = Phi_24(n) where Phi_k(x) is the k-th cyclotomic polynomial.

%H Harry J. Smith, <a href="/A060893/b060893.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_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

%F G.f.: (1-8*x+268*x^2+4264*x^3+15670*x^4+15544*x^5+4348*x^6+232*x^7+x^8)/ (1-x)^9. [_Colin Barker_, Apr 22 2012]

%F a(0)=1, a(1)=1, a(2)=241, a(3)=6481, a(4)=65281, a(5)=390001, a(6)=1678321, a(7)=5762401, a(8)=16773121, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - _Harvey P. Dale_, Nov 03 2014

%p A060893 := proc(n)

%p numtheory[cyclotomic](24,n) ;

%p end proc:

%p seq(A060893(n),n=0..20) ; # _R. J. Mathar_, Feb 11 2014

%t Table[n^8-n^4+1,{n,0,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,1,241,6481,65281,390001,1678321,5762401,16773121},30] (* _Harvey P. Dale_, Nov 03 2014 *)

%o (PARI) { for (n=0, 1000, write("b060893.txt", n, " ", n^8 - n^4 + 1); ) } \\ _Harry J. Smith_, Jul 14 2009

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 05 2001

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)