A178455 Partial sums of floor(2^n/7).

0, 0, 0, 1, 3, 7, 16, 34, 70, 143, 289, 581, 1166, 2336, 4676, 9357, 18719, 37443, 74892, 149790, 299586, 599179, 1198365, 2396737, 4793482, 9586972, 19173952, 38347913, 76695835, 153391679, 306783368, 613566746, 1227133502

Offset: 0

Author

Mircea Merca, Dec 22 2010

Keywords

• nonn
• easy

Comments

Partial sums of A155803.

Examples

			a(6) = 0 + 0 + 0 + 1 + 2 + 4 + 9 = 16.
		

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 (3,-2,1,-3,2).

Crossrefs

Cf. A155803.

Programs

Magma

[Round((12*2^n-14*n-15)/42): n in [0..40]]; // Vincenzo Librandi, Jun 23 2011

Maple

seq(round((6*2^n-7*n-6)/21), n=0..32)

Mathematica

Accumulate[Floor[2^Range[0,40]/7]] (* or *) LinearRecurrence[{3,-2,1,-3,2},{0,0,0,1,3},40] (* Harvey P. Dale, May 02 2015 *)

Formula

a(n) = round((12*2^n - 14*n - 15)/42).

a(n) = round((6*2^n - 7*n - 5)/21).

a(n) = round((6*2^n - 7*n - 10)/21).

a(n) = round((6*2^n - 7*n - 6)/21).

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

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

G.f.: -x^3 / ( (2*x-1)*(1 + x + x^2)*(x-1)^2 ). - R. J. Mathar, Dec 22 2010

a(n) = floor((2^(n+1))/7) - floor((n+1)/3). - Ridouane Oudra, Aug 31 2019