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 A022998 If n is odd then n, otherwise 2n. 80
 0, 1, 4, 3, 8, 5, 12, 7, 16, 9, 20, 11, 24, 13, 28, 15, 32, 17, 36, 19, 40, 21, 44, 23, 48, 25, 52, 27, 56, 29, 60, 31, 64, 33, 68, 35, 72, 37, 76, 39, 80, 41, 84, 43, 88, 45, 92, 47, 96, 49, 100, 51, 104, 53, 108, 55, 112, 57, 116, 59, 120, 61, 124, 63, 128, 65, 132, 67 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also for n > 0: numerator of Sum_{i=1..n} 2/(i*(i+1)), denominator=A026741. - Reinhard Zumkeller, Jul 25 2002 For n > 2: a(n) = gcd(A143051((n-1)^2), A143051(1+(n-1)^2)) = A050873(A000290(n-1), A002522(n-1)). - Reinhard Zumkeller, Jul 20 2008 Partial sums give the generalized octagonal numbers A001082. - Omar E. Pol, Sep 10 2011 Multiples of 4 and odd numbers interleaved. - Omar E. Pol, Sep 25 2011 The Pisano period lengths modulo m appear to be A066043(m). - R. J. Mathar, Oct 08 2011 The partial sums a(n)/A026741(n+1) given by R. Zumkeller in a comment above are 2*n/(n+1) (telescopic sum), and thus converge to 2. - Wolfdieter Lang, Apr 09 2013 a(n) = numerator(H(n,1)), where H(n,1) = 2*n/(n+1) is the harmonic mean of 1 and n. a(n) = 2*n/gcd(2n, n+1) = 2*n/gcd(n+1,2). a(n) = A227041(n,1), n>=1. - Wolfdieter Lang, Jul 04 2013 a(n) = numerator of the mean (2n/(n+1), after reduction), of the compositions of n; denominator is given by A001792(n-1). - Clark Kimberling, Mar 11 2014 A strong divisibility sequence, that is, gcd(a(n), a(m)) = a(gcd(n,m)) for all natural numbers n and m. The sequence of convergents of the 2-periodic continued fraction [0; 1, -4, 1, -4, ...] = 1/(1 - 1/(4 - 1/(1 - 1/(4 - ...)))) begins [0/1, 1/1, 4/3, 3/2, 8/5, 5/3, 12/7, ...]. The present sequence is the sequence of numerators. The sequence of denominators of the continued fraction convergents [1, 1, 3, 2, 5, 3, 7, ...] is A026741, also a strong divisibility sequence. Cf. A203976. - Peter Bala, May 19 2014 a(n) is also the length of the n-th line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized octagonal numbers. - Omar E. Pol, Jul 27 2018 a(n) is the number of petals of the Rhodonea curve r = a*cos(n*theta) or r = a*sin(n*theta). - Matt Westwood, Nov 19 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Rose Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA Denominator of (n+1)*(n-1)*(2*n+1)/(2*n) (for n > 0). a(n+1) = lcm(n, n+2)/n + lcm(n, n+2)/(n+2) for all n >= 1. - Asher Auel (asher.auel(AT)reed.edu), Dec 15 2000 Multiplicative with a(2^e)=2^(e+1), a(p^e)=p^e, p > 2. G.f. x(x^2+4x+1)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003 a(n) = 3n/2 + n(-1)^n/2 = n(3+(-1)^n)/2. - Paul Barry, Sep 04 2003 a(n) = A059029(n-1)+1 = A043547(n+2)-2. a(n)*a(n+3) = -4 + a(n+1)*a(n+2). a(n) = n*(((n+1) mod 2) + 1) = n^2 + 2n - 2n*floor((n+1)/2). - William A. Tedeschi, Feb 29 2008 a(n) = denominator((n+1)/(2*n)) for n >= 1; A026741(n+1) = numerator((n+1)/(2*n)) for n >= 1. - Johannes W. Meijer, Jun 18 2009 a(n) = 2*a(n-2) - a(n-4). Dirichlet g.f. zeta(s-1)*(1+2^(1-s)). - R. J. Mathar, Mar 10 2011 a(n) = n * (2 - n mod 2) = n * A000034(n+1). - Reinhard Zumkeller, Mar 31 2012 a(n) = floor(2n/(1+(n mod 2))). - Wesley Ivan Hurt, Dec 13 2013 From Ilya Gutkovskiy, Mar 16 2017: (Start) E.g.f.: x*(2*sinh(x) + cosh(x)). It appears that a(n) is the period of the sequence k*(k + 1)/2 mod n. (End) MAPLE A022998 := proc(n) if type(n, 'odd') then n ; else 2*n; end if; end proc: # R. J. Mathar, Mar 10 2011 MATHEMATICA Table[n (3 + (-1)^n)/2, {n, 0, 100}] (* Wesley Ivan Hurt, Dec 13 2013 *) Table[If[OddQ[n], n, 2n], {n, 0, 150}] (* or *) Riffle[ 2*Range[ 0, 150, 2], Range[ 1, 150, 2]] (* Harvey P. Dale, Feb 06 2017 *) PROG (PARI) a(n)=if(n%2, n, 2*n) (MAGMA) [((-1)^n+3)*n/2: n in [0..70]]; // Vincenzo Librandi, Sep 17 2011 (Haskell) a022998 n = a000034 (n + 1) * n a022998_list = zipWith (*) [0..] \$ tail a000034_list -- Reinhard Zumkeller, Mar 31 2012 CROSSREFS Cf. A059026. Column 4 of A195151. - Omar E. Pol, Sep 25 2011 Cf. A000034, A001082 (partial sums). Cf. A227041 (first column). - Wolfdieter Lang, Jul 04 2013 Cf. A026741, A203976. Sequence in context: A263616 A280166 A257088 * A082895 A086938 A007015 Adjacent sequences:  A022995 A022996 A022997 * A022999 A023000 A023001 KEYWORD nonn,easy,mult AUTHOR EXTENSIONS More terms from Michael Somos, Aug 07 2000 STATUS approved

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Last modified March 29 18:26 EDT 2020. Contains 333116 sequences. (Running on oeis4.)