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A161707
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(4*n^3 - 9*n^2 + 11*n + 3)/3.
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18
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1, 3, 7, 21, 53, 111, 203, 337, 521, 763, 1071, 1453, 1917, 2471, 3123, 3881, 4753, 5747, 6871, 8133, 9541, 11103, 12827, 14721, 16793, 19051, 21503, 24157, 27021, 30103, 33411, 36953, 40737, 44771, 49063, 53621, 58453, 63567, 68971, 74673
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| {a(k): 0 <= k < 4} = divisors of 21:
a(n) = A027750(A006218(20) + k + 1), 0 <= k < A000005(21).
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LINKS
| R. Zumkeller, Enumerations of Divisors
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n) = C(n,0) + 2*C(n,1) + 2*C(n,2) + 8*C(n,3).
G.f.: (7x^3+x^2-x+1)/(x-1)^4 [From Harvey P. Dale, Mar 28 2011]
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EXAMPLE
| Differences of divisors of 21 to compute the coefficients of their interpolating polynomial, see formula:
1 ... 3 ... 7 ... 21
.. 2 ... 4 .. 14
..... 2 .. 10
........ 8.
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MATHEMATICA
| Table[(4n^3-9n^2+11n+3)/3, {n, 0, 40}] (* or *)
CoefficientList[Series[(7x^3+x^2-x+1)/(x-1)^4, {x, 0, 60}], x](* From Harvey P. Dale, Mar 28 2011 *)
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PROG
| (MAGMA)[(4*n^3 - 9*n^2 + 11*n + 3)/3: n in [0..50]]; [From Vincenzo Librandi, Dec 27 2010]
(PARI) a(n)=(4*n^3-9*n^2+11*n)/3+1 \\ Charles R Greathouse IV, Jul 16, 2011
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CROSSREFS
| Sequence in context: A036569 A018303 A098545 * A192068 A151267 A091489
Adjacent sequences: A161704 A161705 A161706 * A161708 A161709 A161710
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009
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