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A080871
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a(n)*a(n+3) - a(n+1)*a(n+2) = 3, given a(0)=a(1)=1, a(2)=4.
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6
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1, 1, 4, 7, 31, 55, 244, 433, 1921, 3409, 15124, 26839, 119071, 211303, 937444, 1663585, 7380481, 13097377, 58106404, 103115431, 457470751, 811826071, 3601659604, 6391493137, 28355806081, 50320119025, 223244789044
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (3 + a(n-1)*a(n-2))/a(n-3) for n>2.
G.f.: (-x^3 - 4*x^2 + x + 1)/(x^4 - 8*x^2 + 1)
a(n) = (0.25 + sqrt(10)/20)*(sqrt(4 + sqrt(15)))^n + (0.25 + sqrt(10)/20)*(sqrt(4 - sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - sqrt(4 + sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(4 - sqrt(15))))^n. [Richard Choulet, Dec 06 2008]
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MATHEMATICA
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RecurrenceTable[{a[0]==a[1]==1, a[2]==4, a[n]==(3+a[n+1]a[n+2])/a[n+3]}, a, {n, 30}] (* Harvey P. Dale, Jun 08 2017 *)
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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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