A084380 a(n) = n^3 + 2.
2, 3, 10, 29, 66, 127, 218, 345, 514, 731, 1002, 1333, 1730, 2199, 2746, 3377, 4098, 4915, 5834, 6861, 8002, 9263, 10650, 12169, 13826, 15627, 17578, 19685, 21954, 24391, 27002, 29793, 32770, 35939, 39306, 42877, 46658, 50655, 54874, 59321, 64002
Offset: 0
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).
Crossrefs
Cf. sequences for n^3+7, n^3+17, n^3+3.
Essentially the same as A034324.
Programs
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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
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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 *)
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PARI
n3pm(n,m=2) = { for(x=0,n,y=x^3+m; print1(y,", ")) }
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
Extensions
Extended to offset 0 by R. J. Mathar, Feb 16 2011
Comments