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%I #8 Jan 22 2014 05:06:05
%S 1,1,1,3,7,31,331,12795,4642051,60935796571,283646808320375611,
%T 17285560913056915909539455163,
%U 4902995236325455290013100337511909917402705547
%N a(n)=a(n-1)*a(n-2)*a(n-3)*(1/a(n-1)+1/a(n-2)+1/a(n-3)) starting with a(1)=a(2)=a(3)=1.
%C Using the simplified formula which extends the original one to terms that may be zero, one could prefix the values (1, 1, 0), cf. A121810. See also A203761 and references therein. - _M. F. Hasler_, Jan 01 2013
%F a(n) tends towards a(n-1)^phi and 1.22376...^(phi^n) where phi=(1+sqrt(5))/2=1.6180339887...
%F a(n)=a(n-1)*a(n-2)+a(n-3)*a(n-1)+a(n-2)*a(n-3). - _M. F. Hasler_, Jan 01 2013
%e a(7)=31*7*3*(1/31+1/7+1/3)=331.
%t RecurrenceTable[{a[n]==a[n-1]*a[n-2]+a[n-3]*a[n-1]+a[n-2]*a[n-3],a[1]==1,a[2]==1,a[3]==1},a[n],{n,1,15}] (* _Vaclav Kotesovec_, Jan 20 2014 *)
%Y Cf. A074046.
%K nonn
%O 1,4
%A _Henry Bottomley_, Aug 14 2002
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