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 A173173 a(n) = ceiling(Fibonacci(n)/2). 10
 0, 1, 1, 1, 2, 3, 4, 7, 11, 17, 28, 45, 72, 117, 189, 305, 494, 799, 1292, 2091, 3383, 5473, 8856, 14329, 23184, 37513, 60697, 98209, 158906, 257115, 416020, 673135, 1089155, 1762289, 2851444, 4613733, 7465176, 12078909, 19544085, 31622993, 51167078, 82790071 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also the independence number of the n-Fibonacci cube graph. - Eric W. Weisstein, Sep 06 2017 Also the edge cover number of the (n-2)-Fibonacci cube graph. - Eric W. Weisstein, Dec 26 2017 Also the calque covering number of the (n-2)-Fibonacci cube graph. - Eric W. Weisstein, Apr 20 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..280 Eric Weisstein's World of Mathematics, Clique Covering Number Eric Weisstein's World of Mathematics, Edge Cover Number Eric Weisstein's World of Mathematics, Fibonacci Cube Graph Eric Weisstein's World of Mathematics, Independence Number Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,-1). FORMULA a(n) = ceiling(Fibonacci(n)/2). - Mircea Merca, Jan 04 2010 a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) - Joerg Arndt, Apr 24 2011 G.f.: x/(1 - x*(1-x^4)/(1 - x^2*(1-x^5)/(1 - x^3*(1-x^6)/(1 - x^4*(1-x^7)/(1 - x^5*(1-x^8)/(1 - x^6*(1-x^9)/(1 - x^7*(1-x^10)/(1 - x^8*(1-x^11)/(1 - ...))))))))), (continued fraction) - Paul D. Hanna, Jul 08 2013 G.f.: x*(1 - x^2 - x^3) / ((1-x^3)*(1 - x - x^2)). [Paul D. Hanna, Jul 18 2013, from Joerg Arndt's formula] a(n) = A061347(n)/6 +1/3 +A000045(n)/2. - R. J. Mathar, Jul 19 2013 For n > 1, if n == 0 (mod 3) then a(n) = a(n-1) + a(n-2) - 1; otherwise a(n) = a(n-1) + a(n-2). - Franklin T. Adams-Watters, Jun 11 2018 MAPLE with(combinat, fibonacci): seq(ceil(fibonacci(n)/2), n=0..33) # Mircea Merca, Jan 04 2010] MATHEMATICA Table[Fibonacci[n] - Floor[Fibonacci[n]/2], {n, 0, 40}] (* Harvey P. Dale, Jun 09 2013 *) (* Start from Eric W. Weisstein, Sep 06 2017 *) Table[Ceiling[Fibonacci[n]/2], {n, 0, 20}] Ceiling[Fibonacci[Range[0, 20]]/2] LinearRecurrence[{1, 1, 1, -1, -1}, {1, 2, 3, 4, 7}, 20] CoefficientList[Series[(1 + x - 2 x^3 - x^4)/(1 - x - x^2 - x^3 + x^4 + x^5), {x, 0, 20}], x] (* End *) PROG (MAGMA) [Fibonacci(n) - Floor(Fibonacci(n)/2): n in [0..50]]; // Vincenzo Librandi, Apr 24 2011 (PARI) /* Continued Fraction: */ {a(n)=my(CF); CF=1+x; for(k=0, n, CF=1/(1 - x^(n-k+1)*(1 - x^(n-k+4)) *CF +x*O(x^n) )); polcoeff(x*CF, n)} \\ Paul D. Hanna, Jul 08 2013 (PARI) {a(n)=polcoeff( x*(1 - x^2 - x^3) / ((1-x^3)*(1 - x - x^2 +x*O(x^n))), n)} \\ Paul D. Hanna, Jul 18 2013 (PARI) a(n)=(fibonacci(n)+1)\2 \\ Charles R Greathouse IV, Jun 11 2015 CROSSREFS Column m=3 of A185646. Sequence in context: A222026 A293672 A050193 * A303025 A192669 A072164 Adjacent sequences:  A173170 A173171 A173172 * A173174 A173175 A173176 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Nov 22 2010 EXTENSIONS Name simplified using Mircea Merca's formula by Eric W. Weisstein, Sep 06 2017 STATUS approved

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Last modified June 4 11:28 EDT 2020. Contains 334825 sequences. (Running on oeis4.)