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A250309
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a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.
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4
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1, 1, 1, 2, 6, 42, 924, 143220, 488523420, 258285263294520, 465795819523189050504840, 444125576385425970712647062585372630520, 763680920404535561780141108036287312478667174369871222219397040
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OFFSET
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0,4
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LINKS
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FORMULA
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0 = a(n)*(a(n+2) - a(n+3)) + a(n+2)*a(n+2) for all n>=0.
a(n) ~ b * f^(d^n), where b = 0.270887790039424376..., f = c^(2+sqrt(5)) = 1.574173161904651669837597516422779594... and d = (1+sqrt(5))/2. For the constant c = A258113 = 1.11305797590293193285359770716758491... see A007660. - Vaclav Kotesovec, Jan 18 2015
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MATHEMATICA
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RecurrenceTable[{a[n]==a[n-1]*(1 + a[n-1]/a[n-3]), a[0]==1, a[1]==1, a[2]==1}, a, {n, 0, 12}] (* Vaclav Kotesovec, Jan 18 2015 *)
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PROG
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(PARI) {a(n) = if( n<3, n>=0, a(n-1)*(1 + a(n-1)/a(n-3)))};
(Magma) I:=[1, 1, 1]; [n le 3 select I[n] else Self(n-1)*(1 + Self(n-1)/Self(n-3)): n in [1..15]]; // G. C. Greubel, Aug 03 2018
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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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