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A161702
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(-n^3 + 9n^2 - 5n + 3)/3.
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17
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1, 2, 7, 14, 21, 26, 27, 22, 9, -14, -49, -98, -163, -246, -349, -474, -623, -798, -1001, -1234, -1499, -1798, -2133, -2506, -2919, -3374, -3873, -4418, -5011, -5654, -6349, -7098, -7903, -8766, -9689, -10674, -11723, -12838, -14021, -15274
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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 14:
a(n) = A027750(A006218(13) + k + 1), 0 <= k < A000005(14).
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LINKS
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Table of n, a(n) for n=0..39.
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) + 4*C(n,2) - 2*C(n,3).
G.f.: (1-2*x+5*x^2-6*x^3)/(1-x)^4. [Colin Barker, Jan 08 2012]
a(0)=1, a(1)=2, a(2)=7, a(3)=14, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Jun 15 2013
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EXAMPLE
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Differences of divisors of 14 to compute the coefficients of their interpolating polynomial, see formula:
1 ... 2 ... 7 ... 14
.. 1 ... 5 ... 7
..... 4 ... 2
....... -2.
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MATHEMATICA
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Table[(-n^3+9n^2-5n+3)/3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 2, 7, 14}, 40] (* Harvey P. Dale, Jun 15 2013 *)
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PROG
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(MAGMA)[(-n^3 + 9*n^2 - 5*n + 3)/3: n in [0..50]]; [From Vincenzo Librandi, Dec 27 2010]
(PARI) a(n)=(-n^3+9*n^2-5*n+3)/3 \\ 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, A161703, A000127, A161704, A161706-A161708, A161710, A080856, A161711-A161713, A161715, A006261.
Sequence in context: A018363 A187142 A263398 * A114346 A087324 A261246
Adjacent sequences: A161699 A161700 A161701 * A161703 A161704 A161705
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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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