A178706 Partial sums of floor(3^n/5).

0, 1, 6, 22, 70, 215, 652, 1964, 5900, 17709, 53138, 159426, 478290, 1434883, 4304664, 12914008, 38742040, 116226137, 348678430, 1046035310, 3138105950, 9414317871, 28242953636, 84728860932, 254186582820

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..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,-8,8,-7,3).

Formula

a(n) = round((3*3^n - 5*n - 5)/10).

a(n) = floor((3*3^n - 5*n - 3)/10).

a(n) = ceiling((3*3^n - 5*n - 7)/10).

a(n) = round((3*3^n - 5*n - 3)/10).

a(n) = a(n-4) + 8*3^(n-3) - 2, n > 4.

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

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

Example

a(5) = 0 + 1 + 5 + 16 + 48 = 70.

Maple

A178706 := proc(n) add( floor(3^i/5), i=0..n) ; end proc:

Mathematica

Table[Floor[(3^(n+1)-5*n-3)/10], {n, 1, 30}] (* G. C. Greubel, Jan 25 2019 *)

Prog

(Magma) [Round((3*3^n-5*n-5)/10): n in [1..30]]; // Vincenzo Librandi, Jun 21 2011
(PARI) vector(30, n, ((3^(n+1)-5*n-3)/10)\1) \\ G. C. Greubel, Jan 25 2019
(SageMath) [floor((3^(n+1)-5*n-3)/10) for n in (1..30)] # G. C. Greubel, Jan 25 2019

Crossrefs

Sequence in context: A351648 A397080 A171495 * A276779 A159555 A032195

Adjacent sequences: A178703 A178704 A178705 * A178707 A178708 A178709

Keyword

nonn,less

Author

Mircea Merca, Dec 26 2010

Status

approved