A178703 Partial sums of round(3^n/7).

0, 0, 1, 5, 17, 52, 156, 468, 1405, 4217, 12653, 37960, 113880, 341640, 1024921, 3074765, 9224297, 27672892, 83018676, 249056028, 747168085, 2241504257, 6724512773, 20173538320, 60520614960, 181561844880

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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 (5,-8,7,-3).

Formula

a(n) = round((3*3^n - 7)/14).

a(n) = floor((3*3^n - 1)/14).

a(n) = ceiling((3*3^n - 13)/14).

a(n) = a(n-6) + 52*3^(n-5), n > 5.

a(n) = 5*a(n-1) - 8*a(n-2) + 7*a(n-3) - 3*a(n-4), n > 3.

G.f.: x^2/((1 - x)*(1 - 3*x)*(1 - x + x^2)).

a(n) = 3^(n+1)/14 - 1/2 + A174737(n)/7. - R. J. Mathar, Jan 08 2011

Example

a(6) = 0 + 0 + 1 + 4 + 12 + 35 + 104 = 156.

Maple

A178703 := proc(n) add( round(3^i/7), i=0..n) ; end proc:

Mathematica

Table[Floor[(3^(n+1)-1)/14], {n, 0, 30}] (* G. C. Greubel, Jan 25 2019 *)

Prog

(Magma) [Floor((3*3^n-1)/14): n in [0..30]]; // Vincenzo Librandi, May 01 2011
(PARI) vector(30, n, n--; ((3^(n+1)-1)/14)\1) \\ G. C. Greubel, Jan 25 2019
(Sage) [floor((3^(n+1)-1)/14) for n in (0..30)] # G. C. Greubel, Jan 25 2019

Crossrefs

Sequence in context: A190173 A187257 A290186 * A248875 A037544 A090575

Adjacent sequences: A178700 A178701 A178702 * A178704 A178705 A178706

Keyword

nonn,less,easy

Author

Mircea Merca, Dec 28 2010

Status

approved