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A178455
Partial sums of floor(2^n/7).
4
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
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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
KEYWORD
nonn,easy
AUTHOR
_Mircea Merca_, Dec 22 2010
STATUS
approved