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A161708
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a(n) = -n^3 + 7*n^2 - 5*n + 1.
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20
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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
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OFFSET
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0,2
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COMMENTS
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{a(k): 0 <= k < 4} = divisors of 22:
a(n) = A027750(A006218(21) + k + 1), 0 <= k < A000005(22).
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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sign,easy
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AUTHOR
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Reinhard Zumkeller, Jun 17 2009
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STATUS
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approved
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