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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 Adjacent sequences: A179108 A179109 A179110 * A179112 A179113 A179114 KEYWORD nonn AUTHOR Mircea Merca, Jan 04 2011 STATUS approved

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Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)