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 A161710 (-6*n^7 + 154*n^6 - 1533*n^5 + 7525*n^4 - 18879*n^3 + 22561*n^2 - 7302*n + 2520)/2520. 21
 1, 2, 3, 4, 6, 8, 12, 24, 39, -2, -295, -1308, -3980, -9996, -22150, -44808, -84483, -150534, -256001, -418588, -661806, -1016288, -1521288, -2226376, -3193341, -4498314, -6234123, -8512892, -11468896, -15261684, -20079482, -26142888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS {a(k): 0 <= k < 8} = divisors of 24: a(n) = A027750(A006218(23) + k + 1), 0 <= k < A000005(24). LINKS 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 (8,-28,56,-70,56,-28,8,-1). FORMULA a(n) = C(n,0) + C(n,1) + C(n,4) - 3*C(n,5) + 8*C(n,6) - 12*C(n,7). G.f.: (1-6*x+15*x^2-20*x^3+16*x^4-12*x^5+18*x^6-24*x^7)/(1-x)^8. - Bruno Berselli, Jul 17 2011 a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=6, a(5)=8, a(6)=12, a(7)=24, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+ 8*a(n-7)- a(n-8). - Harvey P. Dale, Jul 15 2012 EXAMPLE Differences of divisors of 24 to compute the coefficients of their interpolating polynomial, see formula: 1 ... 2 ... 3 ... 4 ... 6 ... 8 .. 12 .. 24 .. 1 ... 1 ... 1 ... 2 ... 2 ... 4 .. 12 ..... 0 ... 0 ... 1 ... 0 ... 2 ... 8 ........ 0 ... 1 .. -1 ... 2 ... 6 ........... 1 .. -2 ... 3 ... 4 ............. -3 ... 5 ... 1 ................. 8 .. -4 .................. -12. MATHEMATICA Table[(-6n^7+154n^6-1533n^5+7525n^4-18879n^3+22561n^2-7302n+2520)/2520, {n, 0, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 3, 4, 6, 8, 12, 24}, 40] (* Harvey P. Dale, Jul 15 2012 *) PROG (MAGMA) [(-6*n^7 + 154*n^6 - 1533*n^5 + 7525*n^4 - 18879*n^ 3 + 22561*n^2 - 7302*n + 2520)/2520: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011 (Python) A161710_list, m = [1], [-12, 80, -223, 333, -281, 127, -23, 1] for _ in range(1, 10**2): ....for i in range(7): ........m[i+1]+= m[i] ....A161710_list.append(m[-1]) # Chai Wah Wu, Nov 09 2014 (PARI) a(n)=(-6*n^7+154*n^6-1533*n^5+7525*n^4-18879*n^3+22561*n^2-7302*n+2520)/2520 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A080856, A161711, A161712, A161713, A161715, A006261, A018253, A161700, A161856. Sequence in context: A018597 A018623 A018703 * A018758 A068597 A294342 Adjacent sequences:  A161707 A161708 A161709 * A161711 A161712 A161713 KEYWORD sign,easy AUTHOR Reinhard Zumkeller, Jun 17 2009 STATUS approved

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Last modified December 11 01:49 EST 2018. Contains 318049 sequences. (Running on oeis4.)