A238243 A recursive sequence: a(n) = Fibonacci(n)*a(n-1) + 2.

1, 3, 8, 26, 132, 1058, 13756, 288878, 9821854, 540201972, 48077975510, 6923228473442, 1613112234311988, 608143312335619478, 370967420524727881582, 366144844057906419121436, 584733315960476551336933294, 1510950888441871408654635631698

Offset: 1

Author

Vaclav Kotesovec, Feb 20 2014

Keywords

• nonn

Crossrefs

Cf. A176343, A238244, A003266, A101689, A062073, A000045, A139339.

Programs

Mathematica

RecurrenceTable[{a[n]==Fibonacci[n]*a[n-1]+2,a[1]==1},a,{n,1,20}]

Formula

a(n) ~ c * ((1+sqrt(5))/2)^(n^2/2+n/2) / 5^(n/2), where c = A062073 * (2*A101689-1) = 5.4087126382942177293... is product of Fibonacci factorial constant (see A062073) and -1+2*sum_{n>=1} 1/product(A000045(k), k=1..n).