A178452 Partial sums of floor(2^n/5).

0, 0, 1, 4, 10, 22, 47, 98, 200, 404, 813, 1632, 3270, 6546, 13099, 26206, 52420, 104848, 209705, 419420, 838850, 1677710, 3355431, 6710874, 13421760, 26843532, 53687077, 107374168, 214748350, 429496714, 858993443, 1717986902

Offset: 1

Author

Mircea Merca, Dec 22 2010

Keywords

• nonn
• easy

Comments

Partial sums of A077854(n-3).

Examples

			a(5) = 0 + 0 + 1 + 3 + 6 = 10.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..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,-6,6,-5,2).

Crossrefs

Cf. A077854.

Programs

Magma

[Floor((4*2^n-5*n-3)/10): n in [1..40]]; // Vincenzo Librandi, Jun 23 2011

Maple

seq(round((4*2^n-5*n-4)/10), n=1..50)

Mathematica

CoefficientList[Series[x^2 / ((1 - 2 x) (1 + x^2) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
Accumulate[Floor[2^Range[40]/5]] (* or *) LinearRecurrence[{4,-6,6,-5,2},{0,0,1,4,10},40] (* Harvey P. Dale, Oct 09 2018 *)

Formula

a(n) = round((4*2^n - 5*n - 5)/10).

a(n) = floor((4*2^n - 5*n - 3)/10).

a(n) = ceiling((4*2^n - 5*n - 7)/10).

a(n) = round((4*2^n - 5*n - 4)/10).

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

From Bruno Berselli, Jan 18 2011: (Start)

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

a(n) = (4*2^n - 5*n - 5 + A057077(n)*A000034(n))/10.

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