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A072877
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a(1) = a(2) = a(3) = a(4) = 1; a(n) = (a(n-1)*a(n-3) + a(n-2)^4)/a(n-4).
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5
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1, 1, 1, 1, 2, 3, 19, 119, 65339, 67258454, 959259994615659593, 171965197021698738644442682357, 12959040525296547835480490169418622922155526267774117749963303914461
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OFFSET
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1,5
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COMMENTS
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A variation of a Somos-4 sequence with a(n-2)^4 in place of a(n-2)^2.
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LINKS
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FORMULA
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It appears that, for n >= 1,
a(n) = ceiling(e^(c0*x^n + d0/x^n)) if n is even,
ceiling(e^(c1*x^n + d1/x^n)) if n is odd,
where
x = sqrt(2 + sqrt(3)) = (sqrt(2) + sqrt(6))/2
c0 = 0.024915247166055931001426396817534982995670642690...
c1 = 0.029604794868229453467890216788323427656809346011...
d0 = -10.535089427608481105514469573411011428431309483956...
d1 = -2.856773870202800001336732759121362374871088274450...
(End)
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MAPLE
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L[0]:=0; L[1]:=0; L[2]:=0; L[3]:=0; for n from 0 to 4000 do L[n+4]:=evalf(ln(1+exp(L[n+3]+L[n+1]-4*L[n+2]))+4*L[n+2]-L[n]): od: for n from 3990 to 4000 do print(evalf(ln(L[n+4])/(n+4))): od: #Note: L[n] is log(a[n]) # Andrew Hone, Nov 15 2005
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MATHEMATICA
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nxt[{a_, b_, c_, d_}]:={b, c, d, (d*b+c^4)/a}; NestList[nxt, {1, 1, 1, 1}, 15][[All, 1]] (* Harvey P. Dale, Jun 01 2022 *)
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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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