A100104 a(n) = n^3 - n^2 + 1.

1, 1, 5, 19, 49, 101, 181, 295, 449, 649, 901, 1211, 1585, 2029, 2549, 3151, 3841, 4625, 5509, 6499, 7601, 8821, 10165, 11639, 13249, 15001, 16901, 18955, 21169, 23549, 26101, 28831, 31745, 34849, 38149, 41651, 45361, 49285, 53429, 57799, 62401, 67241, 72325

Offset: 0

Author

N. J. A. Sloane, Jan 12 2005

Keywords

• nonn
• easy

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

a(n) = A100104(n+1) - A100104(n). - Reinhard Zumkeller, Jul 07 2012

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).

Crossrefs

Cf. A162611. - Vincenzo Librandi, May 27 2010

Cf. A049451 (first differences).

Programs

Haskell

a049451 n = n * (3 * n + 1)  -- Reinhard Zumkeller, Jul 07 2012

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 *)

PARI

a(n)=n^3-n^2+1 \\ Charles R Greathouse IV, Oct 07 2015

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)