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(Fibonacci(n+2)/3 + 3*n/8 - 1/24).
a(n) = floor(Fibonacci(n+2)/3 + 3*n/8 + 1/4).
a(n) = ceiling(Fibonacci(n+2)/3 + 3*n/8 - 1/3).
a(n) = a(n-8) + Fibonacci(n-1) + Fibonacci(n-3) + 3, n > 7.
a(n) = 2*a(n-1) - a(n-3) + a(n-8) - 2*a(n-9) + a(n-11), n > 10.
G.f.: (x^9 + x^8 + x^4 + x^3 - x)/((x+1)*(x^2+1)*(x^2+x-1)*(x-1)^2*(x^4+1)).
a(n) = -1/16 + 3*n/8 - (-1)^n/16 + Fibonacci(n+2)/3 - A057077(n)/8 + (-1)^floor((n-1)/4)*A093148(n+1)/12. - R. J. Mathar, Jan 08 2011
EXAMPLE
a(9) = 0 + 1 + 1 + 1 + 1 + 2 + 3 + 5 + 7 + 12 = 33.
MAPLE
A179041 := proc(n) add( ceil(combinat[fibonacci](i)/3), i=0..n) ; end proc:
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved