A239745 a(n) = (3*2^(n+2) + n*(n+5))/2 - 6.

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

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.

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

L. B. W. Jolley, Summation of Series, Dover, 1961, p. 12 (series n. 64).

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,changed

Author

Bruno Berselli, Mar 28 2014

Status

approved