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A161701 a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120. 20
1, 2, 3, 4, 6, 12, 28, 64, 135, 262, 473, 804, 1300, 2016, 3018, 4384, 6205, 8586, 11647, 15524, 20370, 26356, 33672, 42528, 53155, 65806, 80757, 98308, 118784, 142536, 169942, 201408, 237369, 278290, 324667, 377028, 435934, 501980, 575796, 658048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 6} = divisors of 12:

a(n) = A027750(A006218(11) + k + 1), 0 <= k < A000005(12).

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 (6,-15,20,-15,6,-1).

FORMULA

a(n) = C(n,0) + C(n,1) + C(n,4) + C(n,5).

G.f.: (1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6. - Colin Barker, Aug 20 2012

EXAMPLE

Differences of divisors of 12 to compute the coefficients of their interpolating polynomial, see formula:

  1     2     3     4     6    12

     1     1     1     2     6

        0     0     1     4

           0     1     3

              1     2

                 1

MAPLE

A161701:=n->(n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120: seq(A161701(n), n=0..60); # Wesley Ivan Hurt, Jul 16 2017

MATHEMATICA

CoefficientList[Series[(1-4*x+6*x^2-4*x^3+2*x^4)/(1-x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)

PROG

(MAGMA) [(n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

(PARI) a(n)=(n^5-5*n^4+5*n^3+5*n^2+114*n+120)/120 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715.

Sequence in context: A018369 A214570 A078495 * A038504 A275448 A018405

Adjacent sequences:  A161698 A161699 A161700 * A161702 A161703 A161704

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified July 21 02:59 EDT 2017. Contains 289629 sequences.