login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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