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 A161713 a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40. 21
 1, 2, 4, 7, 14, 28, 49, 71, 79, 46, -70, -329, -812, -1624, -2897, -4793, -7507, -11270, -16352, -23065, -31766, -42860, -56803, -74105, -95333, -121114, -152138, -189161, -233008, -284576, -344837, -414841, -495719, -588686, -695044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS {a(k): 0 <= k < 6} = divisors of 28: a(n) = A027750(A006218(27) + k + 1), 0 <= k < A000005(28). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Reinhard Zumkeller, Enumerations of Divisors Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = C(n,0) + C(n,1) + C(n,2) + 3*C(n,4) - 3*C(n,5). G.f.: -(-1+4*x-7*x^2+7*x^3-7*x^4+7*x^5)/(-1+x)^6. - R. J. Mathar, Jun 18 2009 a(0)=1, a(1)=2, a(2)=4, a(3)=7, a(4)=14, a(5)=28, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jan 14 2014 EXAMPLE Differences of divisors of 28 to compute the coefficients of their interpolating polynomial, see formula: 1 2 4 7 14 28 1 2 3 7 14 1 1 4 7 0 3 3 3 0 -3 MATHEMATICA Table[(-n^5+15n^4-65n^3+125n^2-34n)/40+1, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 4, 7, 14, 28}, 40] (* Harvey P. Dale, Jan 14 2014 *) PROG (Magma) [(-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011 (PARI) a(n)=(-n^5+15*n^4-65*n^3+125*n^2-34*n+40)/40 \\ Charles R Greathouse IV, Sep 24 2015 (Python) def A161713(n): return n*(n*(n*(n*(15 - n) - 65) + 125) - 34)//40 + 1 # Chai Wah Wu, Dec 16 2021 CROSSREFS Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A018254, A058331, A080856, A086514, A161700, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161715, A161856. Sequence in context: A218341 A018660 A018692 * A018330 A068060 A239791 Adjacent sequences: A161710 A161711 A161712 * A161714 A161715 A161716 KEYWORD sign,easy AUTHOR Reinhard Zumkeller, Jun 17 2009 STATUS approved

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Last modified May 28 15:59 EDT 2023. Contains 363019 sequences. (Running on oeis4.)