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A050512
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a(n)=(a(n-1)a(n-3)-a(n-2)^2)/a(n-4), a(0)=0, a(1)=a(2)=a(3)=1, a(4)=-1.
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5
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0, 1, 1, 1, -1, -2, -3, -1, 7, 11, 20, -19, -87, -191, -197, 1018, 2681, 8191, -5841, -81289, -261080, -620551, 3033521, 14480129, 69664119, -2664458, -1612539083, -7758440129, -37029252553, 181003520899, 1721180313660
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Contribution from Paul Barry (pbarry(AT)wit.ie), May 31 2010: (Start)
a(n+1) is (-1)^C(n,2) times the Hankel transform of the sequence with g.f.
1/(1-x/(1+x^2/(1-x^2/(1-2x^2/(1+(3/4)x^2/(1+(2/9)x^2/(1+21)x^2/(1-... where
-1,1,2,-3/4,-2/9,21,... are the x-coordinates of the multiples of z=(0,0) on the
elliptic curve E:y^2-2xy-y=x^3-x. (End)
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..250
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FORMULA
| a(2n+1)=a(n+2)a(n)^3 - a(n-1)a(n+1)^3,
a(2n)=a(n+2)a(n)a(n-1)^2 - a(n)a(n-2)a(n+1)^2.
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MATHEMATICA
| a[n_?OddQ] := a[n] = a[(n-1)/2]^3*a[(n+3)/2] - a[(n-3)/2]*a[(n+1)/2]^3; a[n_?EvenQ] := a[n] = (a[n/2-1]^2*a[n/2+2] - a[n/2-2]*a[n/2+1]^2)*a[n/2]; a[0] = 0; a[1] = a[2] = a[3] = 1; a[4] = -1; Table[a[n], {n, 0, 30}] (* From Jean-François Alcover, Nov 29 2011 *)
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PROG
| (PARI) an=vector(200); for(n=1, 4, an[ n ]=[ 1, 1, 1, -1 ][ n ]); for(n=5, length(an), an[ n ]=(an[ n-1 ]*an[ n-3 ]-an[ n-2 ]^2)/an[ n-4 ]); a(n) =sign(n)*an[ abs(n)+(n==0) ]
(Haskell)
a050512 n = a050512_list !! n
a050512_list = 0 : 1 : 1 : 1 : (-1) : zipWith div (zipWith (-) (zipWith (*)
(drop 4 a050512_list) (drop 2 a050512_list))
(map (^ 2) (drop 3 a050512_list))) (tail a050512_list)
-- Reinhard Zumkeller, Nov 02 2011
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CROSSREFS
| Cf. A006769.
Sequence in context: A121637 A161847 A101175 * A107102 A103364 A104027
Adjacent sequences: A050509 A050510 A050511 * A050513 A050514 A050515
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KEYWORD
| sign,easy,nice
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AUTHOR
| Michael Somos
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