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)/11 + 3*n/5 + 43/110).
a(n) = floor(Fibonacci(n+2)/11 + 3*n/5 + 48/55).
a(n) = ceiling(Fibonacci(n+2)/11 + 3*n/5 - 1/11).
a(n) = a(n-10) + Fibonacci(n-3) + 6, n > 9.
a(n) = 2*a(n-1) - a(n-3) + a(n-10) - 2*a(n-11) + a(n-13), n > 12.
G.f.: x*(-1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10) / ( (1+x)*(x^2 + x - 1)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x-1)^2 ).
EXAMPLE
a(11) = 0 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 4 + 5 + 9 = 28.
MAPLE
A179053 := proc(n) add( ceil(combinat[fibonacci](i)/11) , i=0..n) ; end proc:
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved