A161707 a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3.

1, 3, 7, 21, 53, 111, 203, 337, 521, 763, 1071, 1453, 1917, 2471, 3123, 3881, 4753, 5747, 6871, 8133, 9541, 11103, 12827, 14721, 16793, 19051, 21503, 24157, 27021, 30103, 33411, 36953, 40737, 44771, 49063, 53621, 58453, 63567, 68971, 74673

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• nonn
• easy

Comments

{a(k): 0 <= k < 4} = divisors of 21:

a(n) = A027750(A006218(20) + k + 1), 0 <= k < A000005(21).

Examples

			Differences of divisors of 21 to compute the coefficients of their interpolating polynomial, see formula:
  1     3     7    21
     2     4    14
        2    10
           8
		

Links

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

Crossrefs

Cf. A000005, A006218, A027750.

Programs

Magma

[(4*n^3 - 9*n^2 + 11*n + 3)/3: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A161707:=n->(4*n^3 - 9*n^2 + 11*n + 3)/3: seq(A161707(n), n=0..100); # Wesley Ivan Hurt, Jan 19 2017

Mathematica

Table[(4n^3-9n^2+11n+3)/3,{n,0,40}] (* or *)
CoefficientList[Series[(7x^3+x^2-x+1)/(x-1)^4, {x,0,60}], x] (* Harvey P. Dale, Mar 28 2011 *)

PARI

a(n)=(4*n^3-9*n^2+11*n)/3+1 \\ Charles R Greathouse IV, Jul 16 2011

Formula

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

G.f.: (7*x^3 + x^2 - x + 1)/(x-1)^4. - Harvey P. Dale, Mar 28 2011

E.g.f.: (1/3)*(4*x^3 + 3*x^2 + 6*x + 3)*exp(x). - G. C. Greubel, Jul 16 2017