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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178742 Partial sums of floor(2^n/9). 1
0, 0, 0, 0, 1, 4, 11, 25, 53, 109, 222, 449, 904, 1814, 3634, 7274, 14555, 29118, 58245, 116499, 233007, 466023, 932056, 1864123, 3728258, 7456528, 14913068, 29826148, 59652309, 119304632, 238609279, 477218573, 954437161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Partial sums of A153234.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Index entries for linear recurrences with constant coefficients, signature (4,-5,1,4,-5,2).

FORMULA

a(n) = round((8*2^n - 18*n - 9)/36).

a(n) = floor((4*2^n - 9*n + 2)/18).

a(n) = ceiling((4*2^n - 9*n - 11)/18).

a(n) = round((4*2^n - 9*n - 4)/18).

a(n) = a(n-6) + 7*2^(n-5) - 3, n > 5.

a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 4*a(n-4) - 5*a(n-5) + 2*a(n-6).

G.f.: x^4 / ( (1-2*x)*(1+x)*(1-x+x^2)*(1-x)^2 ).

EXAMPLE

a(6) = 0 + 0 + 0 + 0 + 1 + 3 + 7 = 11.

MAPLE

A178742 := proc(n) add( floor(2^i/9), i=0..n) ; end proc:

MATHEMATICA

CoefficientList[Series[x^4/((1-2x)(1+x)(1-x+x^2)(1-x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)

LinearRecurrence[{4, -5, 1, 4, -5, 2}, {0, 0, 0, 0, 1, 4}, 40] (* Harvey P. Dale, Jan 25 2015 *)

PROG

(Magma) [&+[Floor(2^k/9): k in [0..n]]: n in [0..25]]; // Bruno Berselli, Apr 26 2011

(Magma) I:=[0, 0, 0, 0, 1, 4]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2)+Self(n-3)+4*Self(n-4)-5*Self(n-5)+2*Self(n-6): n in [1..40]]; // Vincenzo Librandi, Mar 26 2014

(PARI) vector(30, n, n--; ((4*2^n-9*n+2)/18)\1) \\ G. C. Greubel, Jan 24 2019

(Sage) [floor((4*2^n-9*n+2)/18) for n in (0..30)] # G. C. Greubel, Jan 24 2019

CROSSREFS

Cf. A153234.

Sequence in context: A266337 A262158 A156127 * A202088 A328937 A328936

Adjacent sequences: A178739 A178740 A178741 * A178743 A178744 A178745

KEYWORD

nonn,less

AUTHOR

Mircea Merca, Dec 26 2010

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 December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)