A161702 a(n) = (-n^3 + 9n^2 - 5n + 3)/3.

1, 2, 7, 14, 21, 26, 27, 22, 9, -14, -49, -98, -163, -246, -349, -474, -623, -798, -1001, -1234, -1499, -1798, -2133, -2506, -2919, -3374, -3873, -4418, -5011, -5654, -6349, -7098, -7903, -8766, -9689, -10674, -11723, -12838, -14021, -15274

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• sign
• easy

Comments

{a(k): 0 <= k < 4} = divisors of 14:

a(n) = A027750(A006218(13) + k + 1), 0 <= k < A000005(14).

Examples

			Differences of divisors of 14 to compute the coefficients of their interpolating polynomial, see formula:
  1     2     7    14
     1     5     7
        4     2
          -2
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• R. Zumkeller, Enumerations of Divisors
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161701, A161703, A161704, A161706-A161708, A161710, A161711-A161713, A161715.

Programs

Magma

[(-n^3 + 9*n^2 - 5*n + 3)/3: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A161702:=n->(-n^3 + 9*n^2 - 5*n + 3)/3: seq(A161702(n), n=0..60); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

Table[(-n^3+9n^2-5n+3)/3,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,2,7,14},40] (* Harvey P. Dale, Jun 15 2013 *)

PARI

a(n)=(-n^3+9*n^2-5*n+3)/3 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = C(n,0) + C(n,1) + 4*C(n,2) - 2*C(n,3).

G.f.: (1-2*x+5*x^2-6*x^3)/(1-x)^4. - Colin Barker, Jan 08 2012

a(0)=1, a(1)=2, a(2)=7, a(3)=14, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Jun 15 2013