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A022998 If n is odd then n else 2n. 60
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{2/(i*(i+1))|1<=i<=n}, 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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index to divisibility sequences

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*(mod(n+1,2)+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 length of 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

N. J. A. Sloane

EXTENSIONS

More terms from Michael Somos, Aug 07 2000

STATUS

approved

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Last modified February 25 13:30 EST 2018. Contains 299654 sequences. (Running on oeis4.)