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A179111 Partial sums of round(Fibonacci(n)/11). 1
0, 0, 0, 0, 0, 0, 1, 2, 4, 7, 12, 20, 33, 54, 88, 143, 233, 378, 613, 993, 1608, 2603, 4213, 6818, 11033, 17853, 28889, 46745, 75637, 122385, 198025, 320413, 518441, 838857, 1357301, 2196161, 3553466, 5749631, 9303101 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
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,-1,0,0,0,0,0,0,1,-2,0,1).
FORMULA
a(n) = round(Fibonacci(n+2)/11 - n/10 - 83/220).
a(n) = floor(Fibonacci(n+2)/11 - n/10 - 4/55).
a(n) = ceiling(Fibonacci(n+2)/11 - n/10 - 15/22).
a(n) = a(n-10) + Fibonacci(n-3) - 1, n > 10.
a(n) = 2*a(n-1) - a(n-3) + a(n-10) - 2*a(n-11) + a(n-13), n > 11.
G.f.: -x^6 / ( (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 + 0 + 0 + 0 + 0 + 0 + 1 + 1 + 2 + 3 + 5 + 8 = 20.
MAPLE
A179111 := proc(n) add( round(combinat[fibonacci](i)/11) , i=0..n) ; end proc:
MATHEMATICA
Accumulate[Round[Fibonacci[Range[0, 40]]/11]] (* or *) LinearRecurrence[ {2, 0, -1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 2, 4, 7, 12, 20, 33}, 40] (* Harvey P. Dale, Aug 19 2017 *)
CROSSREFS
Sequence in context: A006731 A222036 A000071 * A093607 A005182 A329397
KEYWORD
nonn
AUTHOR
Mircea Merca, Jan 04 2011
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)