A178875 Partial sums of round(4^n/9).

0, 0, 2, 9, 37, 151, 606, 2426, 9708, 38835, 155343, 621377, 2485512, 9942052, 39768214, 159072861, 636291449, 2545165803, 10180663218, 40722652878, 162890611520, 651562446087, 2606249784355, 10424999137429, 41699996549724, 166799986198904

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..170

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,-4,1,-5,4).

Formula

a(n) = round((4*4^n - 3*n - 4)/27) = round((8*4^n - 6*n - 17)/54).

a(n) = floor((4*4^n - 3*n - 4)/27).

a(n) = ceiling((4*4^n - 3*n - 13)/27).

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

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

G.f.: (x^3-2*x^2)/((4*x-1)*(x^2+x+1)*(x-1)^2).

Example

a(3)=0+0+2+7=9.

Maple

A178875 := proc(n) add( round(4^i/9), i=0..n) ; end proc:

Mathematica

Accumulate[Round[4^Range[0, 30]/9]] (* Harvey P. Dale, Dec 16 2012 *)

Prog

(Magma) [Floor((4*4^n-3*n-4)/27): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Crossrefs

Sequence in context: A333883 A206374 A037553 * A012493 A106851 A129169

Adjacent sequences: A178872 A178873 A178874 * A178876 A178877 A178878

Keyword

nonn,less

Author

Mircea Merca, Dec 28 2010

Status

approved