OFFSET
0,3
COMMENTS
Partial sums of A173173.
LINKS
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 (2,0,0,-2,0,1).
FORMULA
a(n) = round(Fibonacci(n+2)/2 + (n-1)/3).
a(n) = round(Fibonacci(n+2)/2 + n/3 - 1/2).
a(n) = floor(Fibonacci(n+2)/2 + n/3 - 1/6).
a(n) = ceiling(Fibonacci(n+2)/2 + n/3 - 1/2).
a(n) = a(n-3) + Fibonacci(n)+1, n > 2.
a(n) = 2*a(n-1) - 2*a(n-4) + a(n-6), n > 5.
G.f.: x*(x^3+x^2-1) / ( (x^2+x+1)*(x^2+x-1)*(x-1)^2 ).
EXAMPLE
a(4) = 0 + 1 + 1 + 1 + 2 = 5.
MAPLE
seq(ceil(Fibonacci(n+2)/2+n/3-1/2), n=0..30)
PROG
(PARI) a(n)=(3*fibonacci(n+2)+2*n-1)\6 \\ Charles R Greathouse IV, Nov 02 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved