0,3

All positive divisors of a(n) are congruent to 1, modulo 12. Proof: If p is an odd prime different from 3 then n^4 - n^2 + 1 = 0 (mod p) implies: (a) (2n^2 - 1)^2 = -3 (mod p), whence p = 1 (mod 6); and (b) (n^2 - 1)^2 = -n^2 (mod p), whence p = 1 (mod 4). - Nick Hobson, Nov 13 2006

Appears to be the number of distinct possible sums of a set of n distinct integers between 1 and n^3. Checked up to n = 4. - Dylan Hamilton, Sep 21 2010

Harry J. Smith, Table of n, a(n) for n = 0..1000

John Elias, Illustration of initial terms: chain-linked squares

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

a(n) = Phi_12(n), where Phi_k is the k-th cyclotomic polynomial.

G.f.: (1-4*x+18*x^2+8*x^3+x^4)/(1-x)^5. - Colin Barker, Apr 21 2012

a(n) = (n^2 - 1/2)^2 + 3/4. - Alonso del Arte, Dec 20 2015

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5), for n>4. - Vincenzo Librandi, Dec 20 2015

A060886 := proc(n)

numtheory[cyclotomic](12, n) ;

end proc:

seq(A060886(n), n=0..20) ; # R. J. Mathar, Feb 07 2014

(Range[0, 29]^2 - 1/2)^2 + 3/4 (* Alonso del Arte, Dec 20 2015 *)

Table[n^4 - n^2 + 1, {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2015 *)

(PARI) a(n) = n^4 - n^2 + 1; \\ Harry J. Smith, Jul 14 2009

(Magma) [n^4 - n^2 + 1: n in [0..40]]; /* or */ I:=[1, 1, 13, 73, 241]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Dec 20 2015

Sequence in context: A084218 A175361 A125258 * A081586 A143008 A107963

Adjacent sequences: A060883 A060884 A060885 * A060887 A060888 A060889

nonn,easy

N. J. A. Sloane, May 05 2001

approved