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%I #20 Jun 18 2017 02:17:15
%S 1,5,341,7381,69905,406901,1727605,5884901,17043521,43584805,
%T 101010101,216145205,432988561,820586261,1483357205,2574332101,
%U 4311810305,6999978821,11054078101,17030739605,25664160401,37908820405,54989488181
%N a(n) = n^8 + n^6 + n^4 + n^2 + 1.
%H Harry J. Smith, <a href="/A059839/b059839.txt">Table of n, a(n) for n = 0..1000</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 a(n) = (n^4-n^3+n^2-n+1)*(n^4+n^3+n^2+n+1) = A060884(n)*A053699(n). a(n) = (n^10-1)/(n^2-1), n>1. - _Alexander Adamchuk_, Apr 13 2006
%F G.f.: -(5*x^8 +296*x^7 +4492*x^6 +15332*x^5 +15458*x^4 +4408*x^3 +332*x^2 -4*x +1)/ (x-1)^9. - _Colin Barker_, Nov 05 2012
%t Table[Total[n^(2*Range[4])]+1,{n,0,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,5,341,7381,69905,406901,1727605,5884901,17043521},30] (* _Harvey P. Dale_, Jan 02 2015 *)
%o (PARI) { for (n=0, 1000, f=n^2; write("b059839.txt", n, " ", f^4 + f^3 + f^2 + f + 1); ) } \\ _Harry J. Smith_, Jun 29 2009
%Y Cf. A059830.
%Y Cf. A060884, A053699.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 25 2001
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