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

1,4

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

Links

Table of n, a(n) for n=1..13.

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

Example

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

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 *)

Crossrefs

Cf. A074046.

Sequence in context: A063896 A277028 A156895 * A121810 A081475 A123212

Adjacent sequences: A074044 A074045 A074046 * A074048 A074049 A074050

Keyword

nonn

Author

Henry Bottomley, Aug 14 2002

Status

approved