OFFSET
0,3
COMMENTS
Appears to be the number of possible distinct sums of a set of n distinct integers between 1 and n^2. Checked up to n=6. - Dylan Hamilton, Sep 21 2010
REFERENCES
T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
FORMULA
From Harvey P. Dale, Sep 11 2011: (Start)
a(0)=1, a(1)=1, a(2)=5, a(3)=19, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: (x^3+7*x^2-3*x+1)/(x-1)^4. (End)
MATHEMATICA
f[n_]:=n^3-n^2+1; Table[f[n], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)
Array[#^3-#^2+1&, 50, 0] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 1, 5, 19}, 50] (* Harvey P. Dale, Sep 11 2011 *)
PROG
(Haskell)
a049451 n = n * (3 * n + 1) -- Reinhard Zumkeller, Jul 07 2012
(PARI) a(n)=n^3-n^2+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 12 2005
STATUS
approved