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
Examples
a(6) = 0 + 0 + 1 + 4 + 12 + 35 + 104 = 156.
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).
Programs
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Magma
[Floor((3*3^n-1)/14): n in [0..30]]; // Vincenzo Librandi, May 01 2011
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Maple
A178703 := proc(n) add( round(3^i/7),i=0..n) ; end proc:
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Mathematica
Table[Floor[(3^(n+1)-1)/14], {n,0,30}] (* G. C. Greubel, Jan 25 2019 *) -
PARI
vector(30, n, n--; ((3^(n+1)-1)/14)\1) \\ G. C. Greubel, Jan 25 2019
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Sage
[floor((3^(n+1)-1)/14) for n in (0..30)] # G. C. Greubel, Jan 25 2019
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