A115590 a(0) = 0; a(n) = (1+a(n-1))^3 for n > 0.
0, 1, 8, 729, 389017000, 58871587162270593034051001, 204040901322752673844230437877671861543858084850895762746141813554591014612008
Offset: 0
Links
- Geir Agnarsson, Elie Alhajjar, and Aleyah Dawkins, On locally finite ordered rooted trees and their rooted subtrees, arXiv:2312.11379 [math.CO], 2023.
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
- Index entries for sequences related to rooted trees
Programs
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Mathematica
{0}~Join~RecurrenceTable[{a[n]==(a[n-1]+1)^3, a[0]==1},a,{n,0,8}] (* Vaclav Kotesovec, May 21 2015 *)
Formula
As for A004019, it follows from Aho and Sloane that there is a constant c such that a(n) is the nearest integer to c^(3^n). In fact a(n) = nearest integer to b^(3^n) - 1 where b = 2.0804006677503193521177452323719035237099784935372250879749088464344434056773788...
Extensions
Name edited by Michael De Vlieger, Dec 21 2023
Comments