This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173173 #64 Feb 16 2025 08:33:11
%S A173173 0,1,1,1,2,3,4,7,11,17,28,45,72,117,189,305,494,799,1292,2091,3383,
%T A173173 5473,8856,14329,23184,37513,60697,98209,158906,257115,416020,673135,
%U A173173 1089155,1762289,2851444,4613733,7465176,12078909,19544085,31622993,51167078,82790071
%N A173173 a(n) = ceiling(Fibonacci(n)/2).
%C A173173 Also the independence number of the n-Fibonacci cube graph. - _Eric W. Weisstein_, Sep 06 2017
%C A173173 Also the edge cover number of the (n-2)-Fibonacci cube graph. - _Eric W. Weisstein_, Dec 26 2017
%C A173173 Also the calque covering number of the (n-2)-Fibonacci cube graph. - _Eric W. Weisstein_, Apr 20 2019
%H A173173 Vincenzo Librandi, <a href="/A173173/b173173.txt">Table of n, a(n) for n = 0..280</a>
%H A173173 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CliqueCoveringNumber.html">Clique Covering Number</a>
%H A173173 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCoverNumber.html">Edge Cover Number</a>
%H A173173 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciCubeGraph.html">Fibonacci Cube Graph</a>
%H A173173 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependenceNumber.html">Independence Number</a>
%H A173173 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,-1).
%F A173173 a(n) = ceiling(Fibonacci(n)/2). - _Mircea Merca_, Jan 04 2010
%F A173173 a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) - _Joerg Arndt_, Apr 24 2011
%F A173173 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
%F A173173 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]
%F A173173 a(n) = A061347(n)/6 +1/3 +A000045(n)/2. - _R. J. Mathar_, Jul 19 2013
%F A173173 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
%p A173173 with(combinat,fibonacci): seq(ceil(fibonacci(n)/2),n=0..33) # _Mircea Merca_, Jan 04 2010
%t A173173 Table[Fibonacci[n] - Floor[Fibonacci[n]/2], {n, 0, 40}] (* _Harvey P. Dale_, Jun 09 2013 *)
%t A173173 (* Start from _Eric W. Weisstein_, Sep 06 2017 *)
%t A173173 Table[Ceiling[Fibonacci[n]/2], {n, 0, 20}]
%t A173173 Ceiling[Fibonacci[Range[0, 20]]/2]
%t A173173 LinearRecurrence[{1, 1, 1, -1, -1}, {1, 2, 3, 4, 7}, 20]
%t A173173 CoefficientList[Series[(1 + x - 2 x^3 - x^4)/(1 - x - x^2 - x^3 + x^4 + x^5), {x, 0, 20}], x]
%t A173173 (* End *)
%o A173173 (Magma) [Fibonacci(n) - Floor(Fibonacci(n)/2): n in [0..50]]; // _Vincenzo Librandi_, Apr 24 2011
%o A173173 (PARI) /* Continued Fraction: */
%o A173173 {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
%o A173173 (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
%o A173173 (PARI) a(n)=(fibonacci(n)+1)\2 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y A173173 Column m=3 of A185646.
%K A173173 nonn,easy
%O A173173 0,5
%A A173173 _Roger L. Bagula_, Nov 22 2010
%E A173173 Name simplified using _Mircea Merca_'s formula by _Eric W. Weisstein_, Sep 06 2017