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A105236
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a(n+5) = (a(n+4)*a(n+1) + 2*a(n+3)*a(n+2))/a(n).
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1
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1, 1, 1, 1, 1, 3, 5, 11, 41, 233, 689, 5337, 49081, 458299, 3603685, 93208147, 1476087601, 27470407569, 816413467841, 43620306030449, 1172020019840081, 70063780891581107, 5804382690927311525, 511286588817798535899
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OFFSET
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0,6
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COMMENTS
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This is a bilinear recurrence of Somos 5 type, hence the terms a(n) are associated with a sequence of points P_n = P_0 + n*P on an elliptic curve E. In this case the curve E has integral j-invariant j=10976.
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LINKS
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MATHEMATICA
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RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==1, a[n]==(2 a[-3+n] a[-2+n]+a[-4+n] a[-1+n])/a[-5+n]}, a, {n, 30}] (* Harvey P. Dale, Sep 15 2013 *)
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PROG
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(Magma) [n le 5 select 1 else (Self(n-1)*Self(n-4) +2*Self(n-2)*Self(n-3))/Self(n-5): n in [1..41]]; // G. C. Greubel, Nov 26 2022
(SageMath)
@CachedFunction
if (n<5): return 1
else: return (a(n-1)*a(n-4) +2*a(n-2)*a(n-3))/a(n-5)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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