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A178875
Partial sums of round(4^n/9).
1
0, 0, 2, 9, 37, 151, 606, 2426, 9708, 38835, 155343, 621377, 2485512, 9942052, 39768214, 159072861, 636291449, 2545165803, 10180663218, 40722652878, 162890611520, 651562446087, 2606249784355, 10424999137429, 41699996549724, 166799986198904
OFFSET
0,3
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*4^n - 3*n - 4)/27) = round((8*4^n - 6*n - 17)/54).
a(n) = floor((4*4^n - 3*n - 4)/27).
a(n) = ceiling((4*4^n - 3*n - 13)/27).
a(n) = a(n-3) + (7*4^(n-2) - 1)/3, n > 2.
a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5), n > 4.
G.f.: (x^3-2*x^2)/((4*x-1)*(x^2+x+1)*(x-1)^2).
EXAMPLE
a(3)=0+0+2+7=9.
MAPLE
A178875 := proc(n) add( round(4^i/9), i=0..n) ; end proc:
MATHEMATICA
Accumulate[Round[4^Range[0, 30]/9]] (* Harvey P. Dale, Dec 16 2012 *)
PROG
(Magma) [Floor((4*4^n-3*n-4)/27): n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
CROSSREFS
Sequence in context: A373909 A206374 A037553 * A012493 A106851 A129169
KEYWORD
nonn,less
AUTHOR
Mircea Merca, Dec 28 2010
STATUS
approved