A161708 a(n) = -n^3 + 7*n^2 - 5*n + 1.

1, 2, 11, 22, 29, 26, 7, -34, -103, -206, -349, -538, -779, -1078, -1441, -1874, -2383, -2974, -3653, -4426, -5299, -6278, -7369, -8578, -9911, -11374, -12973, -14714, -16603, -18646, -20849, -23218, -25759, -28478, -31381, -34474, -37763, -41254

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• sign
• easy

Comments

{a(k): 0 <= k < 4} = divisors of 22:

a(n) = A027750(A006218(21) + k + 1), 0 <= k < A000005(22).

Examples

			Differences of divisors of 22 to compute the coefficients of their interpolating polynomial, see formula:
  1     2    11    22
     1     9    11
        8     2
          -6
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Reinhard Zumkeller, Enumerations of Divisors
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161710, A080856, A161711, A161712, A161713, A161715, A006261.

Programs

Magma

[-n^3 + 7*n^2 - 5*n + 1: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011

Mathematica

Table[-n^3+7n^2-5n+1,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,2,11,22},40] (* Harvey P. Dale, Nov 12 2013 *)

PARI

a(n)=-n^3+7*n^2-5*n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = C(n,0) + C(n,1) + 8*C(n,2) - 6*C(n,3).

G.f.: -(-1+2*x-9*x^2+14*x^3)/(-1+x)^4. - R. J. Mathar, Jun 18 2009

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) with a(0)=1, a(1)=2, a(2)=11, a(3)=22. - Harvey P. Dale, Nov 12 2013

E.g.f.: (-x^3 + 4*x^2 + x + 1)*exp(x). - G. C. Greubel, Jul 16 2017