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 A179042 Partial sums of ceiling(Fibonacci(n)/4). 1
 0, 1, 2, 3, 4, 6, 8, 12, 18, 27, 41, 64, 100, 159, 254, 407, 654, 1054, 1700, 2746, 4438, 7175, 11603, 18768, 30360, 49117, 79466, 128571, 208024, 336582, 544592, 881160, 1425738, 2306883, 3732605, 6039472, 9772060 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A074964 A017822 A292772 * A222786 A353405 A156082 Adjacent sequences: A179039 A179040 A179041 * A179043 A179044 A179045 KEYWORD nonn AUTHOR Mircea Merca, Jan 04 2011 STATUS approved

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Last modified January 27 17:21 EST 2023. Contains 359845 sequences. (Running on oeis4.)