OFFSET
0,1
COMMENTS
This sequence contains no square numbers. A proof may be similar to the Hilliard link.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Dorin Andrica and Ovidiu Bagdasar, On k-partitions of multisets with equal sums, The Ramanujan J. (2021) Vol. 55, 421-435.
D. R. Heath-Brown, The largest prime factor of X^3 + 2, Proc. London Math. Soc. (3), 82:3 (2001), pp. 554-596.
Cino Hilliard, Proof that a cube plus 7 cannot be a square
A. J. Irving, The largest prime factor of X^3+2, arXiv:1412.0024 [math.NT], 2014.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: (2 - 5*x + 10*x^2 - x^3) / (x-1)^4 . - R. J. Mathar, Feb 16 2011
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 24 2012
MATHEMATICA
f[n_]:=n^3+2; f[Range[60]] (* Offset 1. *) (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *)
CoefficientList[Series[(2-5*x+10*x^2-x^3)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 24 2012 *)
PROG
(PARI) n3pm(n, m=2) = { for(x=0, n, y=x^3+m; print1(y, ", ")) }
(Magma) I:=[2, 3, 10, 29]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3) -Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 24 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Jun 23 2003
EXTENSIONS
Extended to offset 0 by R. J. Mathar, Feb 16 2011
STATUS
approved