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A161708 a(n) = -n^3 + 7*n^2 - 5*n + 1. 20
1, 2, 11, 22, 29, 26, 7, -34, -103, -206, -349, -538, -779, -1078, -1441, -1874, -2383, -2974, -3653, -4426, -5299, -6278, -7369, -8578, -9911, -11374, -12973, -14714, -16603, -18646, -20849, -23218, -25759, -28478, -31381, -34474, -37763, -41254 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 4} = divisors of 22:

a(n) = A027750(A006218(21) + k + 1), 0 <= k < A000005(22).

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).

FORMULA

a(n) = C(n,0) + C(n,1) + 8*C(n,2) - 6*C(n,3).

G.f.: -(-1+2*x-9*x^2+14*x^3)/(-1+x)^4. - R. J. Mathar, Jun 18 2009

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) with a(0)=1, a(1)=2, a(2)=11, a(3)=22. - Harvey P. Dale, Nov 12 2013

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

EXAMPLE

Differences of divisors of 22 to compute the coefficients of their interpolating polynomial, see formula:

  1     2    11    22

     1     9    11

        8     2

          -6

MATHEMATICA

Table[-n^3+7n^2-5n+1, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 2, 11, 22}, 40] (* Harvey P. Dale, Nov 12 2013 *)

PROG

(MAGMA) [-n^3 + 7*n^2 - 5*n + 1: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011

(PARI) a(n)=-n^3+7*n^2-5*n+1 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161710, A080856, A161711, A161712, A161713, A161715, A006261.

Sequence in context: A218340 A018491 A031010 * A076206 A018563 A018590

Adjacent sequences:  A161705 A161706 A161707 * A161709 A161710 A161711

KEYWORD

sign,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.