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A161708 -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(0)=1, a(1)=2, a(2)=11, a(3)=22, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Nov 12 2013

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

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

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.