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A178452
Partial sums of floor(2^n/5).
2
0, 0, 1, 4, 10, 22, 47, 98, 200, 404, 813, 1632, 3270, 6546, 13099, 26206, 52420, 104848, 209705, 419420, 838850, 1677710, 3355431, 6710874, 13421760, 26843532, 53687077, 107374168, 214748350, 429496714, 858993443, 1717986902
OFFSET
1,4
COMMENTS
Partial sums of A077854(n-3).
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((4*2^n - 5*n - 5)/10).
a(n) = floor((4*2^n - 5*n - 3)/10).
a(n) = ceiling((4*2^n - 5*n - 7)/10).
a(n) = round((4*2^n - 5*n - 4)/10).
a(n) = a(n-4) + 3*2^(n-3) - 2, n > 4.
From Bruno Berselli, Jan 18 2011: (Start)
G.f.: x^3/((1-2*x)*(1+x^2)*(1-x)^2).
a(n) = (4*2^n - 5*n - 5 + A057077(n)*A000034(n))/10.
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-4) - 3*a(n-5) + 2*a(n-6) for n > 6. (End)
EXAMPLE
a(5) = 0 + 0 + 1 + 3 + 6 = 10.
MAPLE
seq(round((4*2^n-5*n-4)/10), n=1..50)
MATHEMATICA
CoefficientList[Series[x^2 / ((1 - 2 x) (1 + x^2) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
Accumulate[Floor[2^Range[40]/5]] (* or *) LinearRecurrence[{4, -6, 6, -5, 2}, {0, 0, 1, 4, 10}, 40] (* Harvey P. Dale, Oct 09 2018 *)
PROG
(Magma) [Floor((4*2^n-5*n-3)/10): n in [1..40]]; // Vincenzo Librandi, Jun 23 2011
CROSSREFS
Cf. A077854.
Sequence in context: A008267 A056112 A118430 * A324536 A137247 A155407
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 22 2010
STATUS
approved