A059839 a(n) = n^8 + n^6 + n^4 + n^2 + 1.

1, 5, 341, 7381, 69905, 406901, 1727605, 5884901, 17043521, 43584805, 101010101, 216145205, 432988561, 820586261, 1483357205, 2574332101, 4311810305, 6999978821, 11054078101, 17030739605, 25664160401, 37908820405, 54989488181, 78459301541, 110266749505, 152832422501

Offset: 0

Author

N. J. A. Sloane, Feb 25 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A059830.

Cf. A060884, A053699.

Programs

Mathematica

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 *)

PARI

a(n) = { my(f=n^2); f^4 + f^3 + f^2 + f + 1 } \\ Harry J. Smith, Jun 29 2009

Formula

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

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