A178874 Partial sums of round(5^n/8).

0, 1, 4, 20, 98, 489, 2442, 12208, 61036, 305177, 1525880, 7629396, 38146974, 190734865, 953674318, 4768371584, 23841857912, 119209289553, 596046447756, 2980232238772, 14901161193850, 74505805969241, 372529029846194

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..160

Index entries for linear recurrences with constant coefficients, signature (6,-4,-6,5).

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Formula

a(n) = round((5*5^n + 4*n - 1)/32) = round((5*5^n + 4*n - 5)/32).

a(n) = floor((5*5^n + 4*n + 3)/32).

a(n) = ceiling((5*5^n + 4*n - 5)/32).

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

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

G.f.: (2*x^2-x)/((x+1)*(5*x-1)*(x-1)^2).

a(n) = (5^(n+1) + 4*n - 4*(-1)^n - 1)/32. - Bruno Berselli, Jan 12 2011

Example

a(2) = 0 + 1 + 3 = 4.

Maple

A178874 := proc(n) add( round(5^i/8), i=0..n) ; end proc:

Mathematica

Accumulate[Round[5^Range[0, 25]/8]]  (* Harvey P. Dale, Feb 18 2011 *)

Prog

(Magma) [Floor((5*5^n+4*n+3)/32): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Crossrefs

Sequence in context: A293710 A098225 A073532 * A103771 A005054 A370536

Adjacent sequences: A178871 A178872 A178873 * A178875 A178876 A178877

Keyword

nonn,less

Author

Mircea Merca, Dec 28 2010

Status

approved