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A161713 a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40. 21
1, 2, 4, 7, 14, 28, 49, 71, 79, 46, -70, -329, -812, -1624, -2897, -4793, -7507, -11270, -16352, -23065, -31766, -42860, -56803, -74105, -95333, -121114, -152138, -189161, -233008, -284576, -344837, -414841, -495719, -588686, -695044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 6} = divisors of 28:

a(n) = A027750(A006218(27) + k + 1), 0 <= k < A000005(28).

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,2) + 3*C(n,4) - 3*C(n,5).

G.f.: -(-1+4*x-7*x^2+7*x^3-7*x^4+7*x^5)/(-1+x)^6. - R. J. Mathar, Jun 18 2009

a(0)=1, a(1)=2, a(2)=4, a(3)=7, a(4)=14, a(5)=28, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jan 14 2014

EXAMPLE

Differences of divisors of 28 to compute the coefficients of their interpolating polynomial, see formula:

  1     2     4     7    14    28

     1     2     3     7    14

        1     1     4     7

           0     3     3

              3     0

                -3

MATHEMATICA

Table[(-n^5+15n^4-65n^3+125n^2-34n)/40+1, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 4, 7, 14, 28}, 40] (* Harvey P. Dale, Jan 14 2014 *)

PROG

(MAGMA) [(-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011

(PARI) a(n)=(-n^5+15*n^4-65*n^3+125*n^2-34*n+40)/40 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A018254, A058331, A080856, A086514, A161700, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161715, A161856.

Sequence in context: A218341 A018660 A018692 * A018330 A068060 A239791

Adjacent sequences:  A161710 A161711 A161712 * A161714 A161715 A161716

KEYWORD

sign,easy,changed

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified July 21 20:44 EDT 2017. Contains 289648 sequences.