OFFSET
0,3
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,-1,0,0,1,-2,0,1).
FORMULA
a(n) = round(Fibonacci(n+2)/4 + n/2).
a(n) = floor(Fibonacci(n+2)/4 + n/2 + 1/4).
a(n) = ceiling(Fibonacci(n+2)/4 + n/2 - 1/4).
a(n) = round(Fibonacci(n+2)/4 + n/2 - 1/4).
a(n) = a(n-6) + Fibonacci(n-1) + 3, n > 5.
a(n) = 2*a(n-1) - a(n-3) + a(n-6) - 2*a(n-7) + a(n-9), n > 8.
G.f.: (x^7 + x^6 + x^4 + x^3 - x)/((x+1)*(x^2 + x + 1)*(x^2 - x + 1)*(x^2 + x - 1)*(x-1)^2).
EXAMPLE
a(7) = 0 + 1 + 1 + 1 + 1 + 2 + 2 + 4 = 12.
MAPLE
A179042 := proc(n) add( ceil(combinat[fibonacci](i)/4), i=0..n) ; end proc:
MATHEMATICA
Accumulate[Ceiling[Fibonacci[Range[0, 40]]/4]] (* or *) LinearRecurrence[ {2, 0, -1, 0, 0, 1, -2, 0, 1}, {0, 1, 2, 3, 4, 6, 8, 12, 18}, 40] (* Harvey P. Dale, May 25 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved