A178704 Partial sums of floor(3^n/7).

0, 0, 1, 4, 15, 49, 153, 465, 1402, 4213, 12648, 37954, 113874, 341634, 1024915, 3074758, 9224289, 27672883, 83018667, 249056019, 747168076, 2241504247, 6724512762, 20173538308, 60520614948, 181561844868

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..700

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,-7,2,5,-7,3).

Formula

a(n) = round((6*3^n - 14*n - 7)/28).

a(n) = floor((6*3^n - 14*n + 2)/28).

a(n) = ceiling((6*3^n - 14*n - 16)/28).

a(n) = round((6*3^n - 14*n - 6)/28).

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

a(n) = 5*a(n-1) - 7*a(n-2) + 2*a(n-3) + 5*a(n-4) - 7*a(n-5) + 3*a(n-6).

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

Example

a(6) = 0 + 0 + 1 + 3 + 11 + 34 + 104 = 153.

Maple

A178704 := proc(n) add( floor(3^i/7), i=0..n) ; end proc:

Mathematica

Table[Floor[(6*3^n-14*n+2)/28], {n, 0, 30}] (* G. C. Greubel, Jan 25 2019 *)

Prog

(Magma) [Round((6*3^n-14*n-7)/28): n in [0..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, n--; ((6*3^n-14*n+2)/28)\1) \\ G. C. Greubel, Jan 25 2019
(Sage) [floor((6*3^n-14*n+2)/28) for n in (0..30)] # G. C. Greubel, Jan 25 2019

Crossrefs

Sequence in context: A093967 A052201 A320460 * A099167 A056337 A053406

Adjacent sequences: A178701 A178702 A178703 * A178705 A178706 A178707

Keyword

nonn,less

Author

Mircea Merca, Dec 26 2010

Status

approved