OFFSET
0,3
COMMENTS
(b^2+c^2)/(bc+1) is an integer if {b,c} are of the form {0,n}, {n,n^3}, {n^3,n^5-n}, {n^5-n,n^7-2n^3}, {n^7-2n^3,n^9-3n^5+n}, etc. for some n, in which case the division results in n^2. Cf. A052530.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = 30*A033455(n-1). [Corrected by Bernard Schott, Mar 16 2021]
a(n) = -n*A024002(n).
a(n) = A000584(n) - n.
O.g.f.: 30x^2(1+x)^2/(1-x)^6. - R. J. Mathar, Aug 19 2008
a(n) = n * (n-1) * (n+1) * (n^2+1). - Bernard Schott, Mar 16 2021
E.g.f.: exp(x)*x^2*(15 + 25*x + 10*x^2 + x^3). - Stefano Spezia, Dec 27 2021
EXAMPLE
a(2) = 32 - 2 = 30.
MATHEMATICA
Table[n^5 - n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)
PROG
(Magma) [n^5-n: n in [0..40]]; // Vincenzo Librandi, May 02 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Apr 18 2001
STATUS
approved