A177881 Partial sums of round(3^n/10).

0, 0, 1, 4, 12, 36, 109, 328, 984, 2952, 8857, 26572, 79716, 239148, 717445, 2152336, 6457008, 19371024, 58113073, 174339220, 523017660, 1569052980, 4707158941, 14121476824, 42364430472, 127093291416

Offset: 0

Author

Mircea Merca, Dec 28 2010

Keywords

• nonn
• less
• easy

Examples

			a(4) = 0 + 0 + 1 + 3 + 8 = 12.
		

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,-4,4,-3).

Crossrefs

Cf. A015577 (bisection of round(3^n/10)).

Programs

Magma

[Round((3*3^n-3)/20): n in [0..30]]; // Vincenzo Librandi, Jun 23 2011

Maple

A177881 := proc(n) add( round(3^i/10),i=0..n) ; end proc:

Mathematica

Table[(3^(n + 1) + (3 - (-1)^n) i^(n (n + 1)) - 5)/20, {n, 0, 25}] (* Bruno Berselli, May 12 2021 *)

PARI

a(n)=(3^(n+1)-1)\20 \\ Charles R Greathouse IV, Jun 23 2011

Formula

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

a(n) = round((3*3^n - 3)/20) = round((3*3^n - 5)/20).

a(n) = floor((3*3^n - 1)/20).

a(n) = ceiling((3*3^n - 9)/20).

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

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

a(n) = (3^(n+1) + (3 - (-1)^n)*i^(n*(n+1)) - 5)/20, where i = sqrt(-1) - Bruno Berselli, May 12 2021