A161703 a(n) = (4*n^3 - 12*n^2 + 14*n + 3)/3.

1, 3, 5, 15, 41, 91, 173, 295, 465, 691, 981, 1343, 1785, 2315, 2941, 3671, 4513, 5475, 6565, 7791, 9161, 10683, 12365, 14215, 16241, 18451, 20853, 23455, 26265, 29291, 32541, 36023, 39745, 43715, 47941, 52431, 57193, 62235, 67565, 73191, 79121

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• nonn
• easy

Comments

{a(k): 0 <= k < 4} = divisors of 15:

a(n) = A027750(A006218(14) + k + 1), 0 <= k < A000005(15).

Examples

			Differences of divisors of 15 to compute the coefficients of their interpolating polynomial, see formula:
  1     3     5    15
     2     2    10
        0     8
           8
		

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, A161702, A161704, A161706-A161708, A161710, A161711-A161713, A161715.

Programs

Magma

[(4*n^3 - 12*n^2 + 14*n + 3)/3: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A161703:=n->(4*n^3 - 12*n^2 + 14*n + 3)/3: seq(A161703(n), n=0..100); # Wesley Ivan Hurt, Jul 16 2017

Mathematica

CoefficientList[Series[(1 - x - x^2 + 9*x^3)/(1 - x)^4, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)
LinearRecurrence[{4,-6,4,-1},{1,3,5,15},50] (* Harvey P. Dale, Oct 04 2024 *)

PARI

a(n)=n*(4*n^2-12*n+14)/3+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

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

G.f.: (1-x-x^2+9*x^3)/(1-x)^4. - Colin Barker, Jan 08 2012