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A174168
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A (1,3) Somos-4 sequence.
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2
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1, 2, 5, 17, 109, 706, 9529, 149057, 3464585, 141172802, 5987285341, 540281496721, 53055650250901, 8453268527614082, 2173247123169247025, 610193552206250342657, 364280506115937098013649, 225791960727416355391439746
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(-2-n), a(n)*a(n-5) = -3*a(n-1])*a(n-4) + 16*a(n-2)*a(n-3) for all n in Z. - Michael Somos, Apr 30 2020
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MAPLE
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if n <=4 then
op(n+1, [1, 2, 5, 17, 109]) ;
else
(procname(n-1)*procname(n-3)+3*procname(n-2)^2)/procname(n-4) ;
end if;
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MATHEMATICA
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RecurrenceTable[{a[0]==1, a[1]==2, a[2]==5, a[3]==17, a[n]==(a[n-1]a[n-3]+ 3a[n-2]^2)/a[n-4]}, a[n], {n, 20}] (* Harvey P. Dale, Oct 25 2011 *)
a[ n_] := Which[n < -1, a[-2 - n], n < 2, {1, 1, 2}[[n + 2]], True, (a[n - 1] a[n - 3] + 3 a[n - 2]^2)/a[n - 4]]; (* Michael Somos, Apr 30 2020 *)
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PROG
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(Haskell)
a174168 n = a174168_list !! n
a174168_list = [1, 2, 5, 17] ++ zipWith div (zipWith (+)
(zipWith (*) (tail a174168_list) (drop 3 a174168_list))
(map ((* 3) . (^ 2)) (drop 2 a174168_list))) a174168_list
(PARI) m=20; v=concat([1, 2, 5, 17], vector(m-4)); for(n=5, m, v[n] = ( v[n-1]*v[n-3] +3*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 25 2018
(Magma) I:=[1, 2, 5, 17]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + 3*Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Sep 25 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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