A178457 Partial sums of floor(2^n/23).
0, 0, 0, 0, 0, 1, 3, 8, 19, 41, 85, 174, 352, 708, 1420, 2844, 5693, 11391, 22788, 45583, 91173, 182353, 364714, 729436, 1458880, 2917768, 5835544, 11671097, 23342203, 46684416, 93368843, 186737697, 373475405, 746950822, 1493901656, 2987803324, 5975606660, 11951213332, 23902426677, 47804853367, 95609706748
Offset: 0
Examples
a(21) = 0 + 0 + 0 + 0 + 0 + 1 + 2 + 5 + 11 + 22 + 44 + 89 + 178 + 356 + 712 + 1424 + 2849 + 5698 + 11397 + 22795 + 45590 + 91180 = 182353.
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,-2,0,0,0,0,0,0,0,0,1,-3,2).
Programs
-
Magma
[Round((22*2^n-92*n-24)/253): n in [0..40]]; // Vincenzo Librandi, Jun 23 2011
-
Maple
seq(round((22*2^n-92*n-22)/253), n=1..40)
-
Mathematica
Accumulate[Floor[2^Range[0,40]/23]] (* or *) LinearRecurrence[{3,-2,0,0,0,0,0,0,0,0,1,-3,2},{0,0,0,0,0,1,3,8,19,41,85,174,352},50] (* Harvey P. Dale, Mar 05 2016 *) -
PARI
a(n)=(44<
Formula
a(n) = round((22*2^n - 92*n - 24)/253).
a(n) = floor((22*2^n - 92*n + 100)/253).
a(n) = ceiling((22*2^n - 92*n - 148)/253).
a(n) = round((22*2^n - 92*n - 22)/253).
a(n) = a(n-11) + 89*2^(n-10) - 4, n > 10.
G.f.: -x^5*(x^6 + x^3 + x^2 + 1)/((x-1)^2*(2*x-1)*(x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). [Colin Barker, Oct 27 2012]