A161711 a(n) = (-4*n^3 + 27*n^2 - 20*n + 3)/3.

1, 2, 13, 26, 33, 26, -3, -62, -159, -302, -499, -758, -1087, -1494, -1987, -2574, -3263, -4062, -4979, -6022, -7199, -8518, -9987, -11614, -13407, -15374, -17523, -19862, -22399, -25142, -28099, -31278, -34687, -38334, -42227, -46374, -50783

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• sign
• easy

Comments

{a(k): 0 <= k < 4} = divisors of 26:

a(n) = A027750(A006218(25) + k + 1), 0 <= k < A000005(26).

Examples

			Differences of divisors of 26 to compute the coefficients of their interpolating polynomial, see formula:
  1     2    13    26
     1    11    13
       10     2
          -8
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• R. 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, A161708, A161710, A080856, A161712, A161713, A161715, A006261.

Programs

Magma

[(-4*n^3 + 27*n^2 - 20*n + 3)/3: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,2,13,26},40] (* Harvey P. Dale, Jul 02 2017 *)

PARI

x='x+O('x^50); Vec((1-2*x+11*x^2-18*x^3)/(1-x)^4) \\ G. C. Greubel, Jul 16 2017

Formula

a(n) = C(n,0) + C(n,1) + 10*C(n,2) - 8*C(n,3).

G.f.: (1-2*x+11*x^2-18*x^3)/(1-x)^4. - Bruno Berselli, Jul 17 2011