A178460 Partial sums of floor(2^n/127).

0, 0, 0, 0, 0, 0, 1, 3, 7, 15, 31, 63, 127, 256, 514, 1030, 2062, 4126, 8254, 16510, 33023, 66049, 132101, 264205, 528413, 1056829, 2113661, 4227326, 8454656, 16909316, 33818636, 67637276

Offset: 1

Author

Mircea Merca, Dec 22 2010

Keywords

• nonn
• easy
• less

Comments

Partials sums of A117302.

Examples

			a(10) = a(3) + 2^4 - 1 = 15.
		

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 (3,-2,0,0,0,0,1,-3,2).

Crossrefs

Cf. A117302.

Programs

Magma

[Round((14*2^n-127*n+75)/889): n in [1..40]]; // Vincenzo Librandi, Jun 21 2011

Maple

A178460 := proc(n) add( floor(2^i/127),i=0..n) ; end proc:

Formula

a(n) = round((14*2^n - 127*n + 75)/889).

a(n) = floor((14*2^n - 127*n + 284)/889).

a(n) = ceiling((14*2^n - 127*n - 134)/889).

a(n) = round((14*2^n - 127*n - 14)/889).

a(n) = a(n-7) + 2^(n-6) - 1, n > 6.

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-7) - 3*a(n-8) + 2*a(n-9), n > 9.

G.f.: -x^7/((2*x-1)*(x-1)^2*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)).

From Seiichi Manyama, Dec 22 2023: (Start)

a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/7).

a(n) = floor(2^(n+1)/127) - floor((n+1)/7). (End)