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 A161707 a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3. 18
 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; text; internal format)
 OFFSET 0,2 COMMENTS {a(k): 0 <= k < 4} = divisors of 21: a(n) = A027750(A006218(20) + k + 1), 0 <= k < A000005(21). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 R. Zumkeller, Enumerations of Divisors Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = C(n,0) + 2*C(n,1) + 2*C(n,2) + 8*C(n,3). G.f.: (7*x^3 + x^2 - x + 1)/(x-1)^4. - Harvey P. Dale, Mar 28 2011 E.g.f.: (1/3)*(4*x^3 + 3*x^2 + 6*x + 3)*exp(x). - G. C. Greubel, Jul 16 2017 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 MAPLE A161707:=n->(4*n^3 - 9*n^2 + 11*n + 3)/3: seq(A161707(n), n=0..100); # Wesley Ivan Hurt, Jan 19 2017 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] (* Harvey P. Dale, Mar 28 2011 *) PROG (MAGMA)[(4*n^3 - 9*n^2 + 11*n + 3)/3: n in [0..50]]; // 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 CROSSREFS Cf. A000005, A006218, A027750. Sequence in context: A036569 A018303 A098545 * A192068 A151267 A262184 Adjacent sequences:  A161704 A161705 A161706 * A161708 A161709 A161710 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, Jun 17 2009 STATUS approved

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