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 A057979 a(n) = 1 for even n and (n-1)/2 for odd n. 15
 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 19, 1, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 34, 1, 35, 1, 36, 1, 37, 1, 38, 1, 39, 1, 40, 1, 41, 1, 42, 1, 43, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(n) = b(n)/c(n) where b(n) = A001405(n+1) - A001405(n), c(n) = gcd(A001405(n+1), A001405(n)). Also the minimal number of disjoint edge-paths into which the complete graph on n edges can be partitioned - Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 19 2001 For n >= 2, number of partitions of n-2 into parts that are distinct mod 2. - Giovanni Resta, Feb 06 2006 Sequence starting with a(3) obeys the rule "smallest positive value such that the ordered pair (a(n-1),a(n)) has not occurred previously", or the rule "smallest positive value such that the ratio a(n-1)/a(n) has not occurred previously". The same subsequence has its ordinal transform equal to itself, shifted left. (The ordinal transform has as its n-th term the number of values in a(1),...,a(n) that are equal to a(n).) - Franklin T. Adams-Watters, Dec 13 2006 Numerators of floor(n/2)/n, n > 0. - Wesley Ivan Hurt, Jun 14 2013 Number of nonisomorphic outer planar graphs of order n >= 3, maximum degree 3, and largest possible size. The size is (3n-2)/2 when n is even and (3n-3)/2 when n is odd. - Christian Barrientos and Sarah Minion, Feb 27 2018 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(n) = (n+1)/4+(3-n)*(-1)^n/4. - Paul Barry, Mar 21 2003, corrected by Hieronymus Fischer, Sep 25 2007 a(n) = (a(n-2) + a(n-3)) / a(n-1). From Paul Barry, Oct 21 2004: (Start) G.f.: (1-x^2+x^3)/((1+x)^2(1-x)^2); a(n) = 2*a(n-2) - a(n-4); a(n) = 0^n + Sum_{k=0..floor((n-2)/2)} C(n-k-2,k) * C(1,n-2k-2). (End) a(n) = gcd(n-1, floor((n-1)/2)). - Paul Barry, May 02 2005 a(n) = binomial((2n-3)/4-(-1)^n/4, (1-(-1)^n)/2). - Paul Barry, Jun 29 2006 G.f.: (x^3-x^2+1)/(1-x^2)^2 = 1 + x^2*G(0) where G(k) = 1 + x*(k+1)/(1 - x/(x + (k+1)/G(k+1) )); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 29 2012 a(n) = binomial(floor(n/2), n mod 2). - Wesley Ivan Hurt, Oct 14 2013 a(n) = 1 - n mod 2 * (1 - floor(n/2)). - Reinhard Zumkeller, Aug 11 2014 a(n) = floor(n/2)^(n mod 2). - Wesley Ivan Hurt, Mar 16 2015 E.g.f.: ((2 + x)*cosh(x) - sinh(x))/2. - Stefano Spezia, Mar 26 2022 EXAMPLE For n=12, C(12,6) - C(11,5) = 924 - 462 = 462, gcd(C(12,6), C(11,5)) = 462, and the quotient is 1. For n=13, C(13,6) - C(12,6) = 792, gcd(C(13,6), C(12,6)) = 132, and the quotient is 6. MAPLE A057979:=n->(n+1)/4+(3-n)*(-1)^n/4; seq(A057979(k), k=0..100); # Wesley Ivan Hurt, Oct 14 2013 MATHEMATICA With[{no=45}, Riffle[Table[1, {no}], Range[0, no-1]]] (* Harvey P. Dale, Feb 18 2011 *) PROG (Haskell) import Data.List (transpose) a057979 n = 1 - rest * (1 - n') where (n', rest) = divMod n 2 a057979_list = concat \$ transpose [repeat 1, [0..]] -- Reinhard Zumkeller, Aug 11 2014 (Magma) [Floor(n/2)^(n mod 2): n in [0..100]]; // Vincenzo Librandi, Mar 17 2015 (PARI) a(n)=if(n%2, n-1, 2)/2 \\ Charles R Greathouse IV, Sep 02 2015 CROSSREFS Cf. A001405, A007879, A059222, A000035, A027656, A037952, A067992, A152271. Sequence in context: A319338 A177815 A007879 * A152271 A133622 A158416 Adjacent sequences:  A057976 A057977 A057978 * A057980 A057981 A057982 KEYWORD nonn,easy AUTHOR Labos Elemer, Nov 13 2000 STATUS approved

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Last modified July 3 23:09 EDT 2022. Contains 355058 sequences. (Running on oeis4.)