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A121881
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a(n) = (4*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(1)=...=a(4)=1.
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2
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1, 1, 1, 1, 5, 21, 109, 2621, 46409, 1290665, 143900249, 10827502009, 1650671059149, 826986635160509, 267834927512726725, 226491424023176449909, 497347467521206399078801, 706331193237960728379843409
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OFFSET
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1,5
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COMMENTS
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This is a (4,1) generalized Somos-4 sequence. - Michael Somos, May 12 2022
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LINKS
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FORMULA
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a(n) = a(5-n) = (-a(n-1)*a(n-4) + 26*a(n-2)*a(n-3))/a(n-5) for all n in Z. - Michael Somos, May 12 2022
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MAPLE
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a:= proc(n) option remember;
if n < 5 then 1
else (4*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
fi;
end proc;
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MATHEMATICA
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a[n_]:= a[n]= If[n<5, 1, (4*a[n-1]a[n-3] + a[n-2]^2)/a[n-4]]; Table[a[n], {n, 30}]
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PROG
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(PARI) my(m=30, v=concat([1, 1, 1, 1], vector(m-4))); for(n=5, m, v[n] = (4*v[n-1]*v[n-3] + v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Oct 08 2019
(Magma) [n lt 5 select 1 else (4*Self(n-1)*Self(n-3) + Self(n-2)^2 )/Self(n-4): n in [1..30]]; // G. C. Greubel, Oct 08 2019
(Sage)
@CachedFunction
def a(n):
if (n<5): return 1
else: return (4*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
(GAP) a:=[1, 1, 1, 1];; for n in [5..30] do a[n]:=(4*a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # G. C. Greubel, Oct 08 2019
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CROSSREFS
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KEYWORD
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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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