OFFSET
1,4
COMMENTS
Partial sums of A077854(n-3).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..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 (4,-6,6,-5,2).
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) = 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
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 22 2010
STATUS
approved