A059830 a(n) = n^6 + n^4 + n^2 + 1.

1, 4, 85, 820, 4369, 16276, 47989, 120100, 266305, 538084, 1010101, 1786324, 3006865, 4855540, 7568149, 11441476, 16843009, 24221380, 34117525, 47176564, 64160401, 85961044, 113614645, 148316260, 191435329, 244531876, 309373429, 387952660, 482505745, 595531444

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A059839.

Cf. A002522, A002523, A024006, A067998.

Programs

Mathematica

Table[(n^2+1)*(n^4+1),{n,0,40}] (* Alexander Adamchuk, Apr 13 2006 *)

PARI

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

Formula

a(n) = (n^2+1)*(n^4+1) = A002522(n)*A002523(n) = A002522(n)*A002522(n^2). a(n) = (n^8-1)/(n^2-1) = -A024006(n)/A067998(n+1), n>1. - Alexander Adamchuk, Apr 13 2006

G.f.: -(4*x^6+57*x^5+309*x^4+274*x^3+78*x^2-3*x+1)/(x-1)^7. - Colin Barker, Nov 05 2012