OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..170
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 (5,-4,1,-5,4).
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
KEYWORD
nonn,less
AUTHOR
Mircea Merca, Dec 28 2010
STATUS
approved