A074047 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.

1, 1, 1, 3, 7, 31, 331, 12795, 4642051, 60935796571, 283646808320375611, 17285560913056915909539455163, 4902995236325455290013100337511909917402705547

Offset: 1

Author

Henry Bottomley, Aug 14 2002

Keywords

• nonn

Comments

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

Examples

			a(7)=31*7*3*(1/31+1/7+1/3)=331.
		

Crossrefs

Cf. A074046.

Programs

Mathematica

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 *)

Formula

a(n) tends towards a(n-1)^phi and 1.22376...^(phi^n) where phi=(1+sqrt(5))/2=1.6180339887...

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