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A022998
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If n is odd then n else 2n.
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44
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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
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
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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
Contribution from Johannes W. Meijer, Jun 18 2009: (Start)
a(n) = denom((n+1)/(2*n)) for n =>1; A026741 (n+1) = numer((n+1)/(2*n)) for n =>1.
(End)
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]
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MAPLE
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A022998 := proc(n) if type(n, 'odd') then n ; else 2*n; end if; end proc: # R. J. Mathar, Mar 10 2011
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PROG
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(PARI) a(n)=if(n%2, n, 2*n)
(Sage) [n/2*power_mod(2, n, 6) for n in xrange(0, 68)] #A [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 03 2009]
(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
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CROSSREFS
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Cf. A059026.
Column 4 of A195151. - Omar E. Pol, Sep 25 2011
Cf. A000034, A001082 (partial sums).
Sequence in context: A092383 A156028 A021232 * A082895 A086938 A126084
Adjacent sequences: A022995 A022996 A022997 * A022999 A023000 A023001
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KEYWORD
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nonn,easy,mult
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Michael Somos, Aug 07 2000.
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STATUS
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approved
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