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 A239745 a(n) = (3*2^(n+2) + n*(n+5))/2 - 6. 1
 0, 9, 25, 54, 108, 211, 411, 804, 1582, 3129, 6213, 12370, 24672, 49263, 98431, 196752, 393378, 786613, 1573065, 3145950, 6291700, 12583179, 25166115, 50331964, 100663638, 201326961, 402653581, 805306794, 1610613192, 3221225959, 6442451463, 12884902440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from 0, partial sums of the numbers of the form 6*2^m + m + 3. After a(5) = 211 and a(17) = 786613, the third prime number is a(557), which has 169 digits. REFERENCES L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 12 (series n. 64). LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA G.f.: x*(9 - 20*x + 10*x^2)/((1 - 2*x)*(1 - x)^3). a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). MATHEMATICA Table[(3 2^(n + 2) + n (n + 5))/2 - 6, {n, 0, 40}] CoefficientList[Series[x (9 - 20 x + 10 x^2)/((1 - 2 x) (1 - x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 29 2014 *) LinearRecurrence[{5, -9, 7, -2}, {0, 9, 25, 54}, 40] (* Harvey P. Dale, Sep 22 2018 *) PROG (Sage) [(3*2^(n+2)+n*(n+5))/2-6 for n in (0..40)] (Magma) [(3*2^(n+2)+n*(n+5))/2-6: n in [0..40]]; (Magma) I:=[0, 9, 25, 54]; [n le 4 select I[n] else 5*Self(n-1)-9*Self(n-2)+7*Self(n-3)-2*Self(n-4): n in [1..35]]; // Vincenzo Librandi, Mar 29 2014 CROSSREFS Sequence in context: A348232 A147160 A336669 * A269440 A234038 A304033 Adjacent sequences: A239742 A239743 A239744 * A239746 A239747 A239748 KEYWORD nonn,easy AUTHOR Bruno Berselli, Mar 28 2014 STATUS approved

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)