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

0,5

Comments

Partial sums of A155803.

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).

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A155803.

Sequence in context: A182615 A181893 A054455 * A281811 A238089 A335713

Adjacent sequences: A178452 A178453 A178454 * A178456 A178457 A178458

Keyword

nonn,easy

Author

Mircea Merca, Dec 22 2010

Status

approved