A092124 a(0) = 2, a(n) = (2^(2^n)+2)*a(n-1) for n>0.

2, 12, 216, 55728, 3652301664, 15686516209310983872, 289365149921256212111714425927549504896, 98465858119637274097902770931519409290135390781788892125023848289699334298368

Offset

0,1

Comments

In binary representation a(n) can be interpreted as an expression to represent n according to John von Neumann's definition of natural numbers: braces are coded as 1 and 0 and the empty set as 10={};

a(n) = (A001146(n)+2)*a(n-1) = 2*(A058891(n)+1)*a(n-1).

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..10

Example

a(3)=55728='1101100110110000' -> {{}{{}}{{}{{}}}} -> {{},{{}},{{},{{}}}} -> {0,{0},{0,{0}}} -> {0,1,{0,1}} -> {0,1,2} -> A001477(3)=3.

Mathematica

RecurrenceTable[{a[0]==2, a[n]==(2^(2^n)+2)a[n-1]}, a, {n, 8}] (* Harvey P. Dale, Nov 15 2020 *)
nxt[{n_, a_}]:={n+1, (2^2^(n+1)+2)a}; NestList[nxt, {0, 2}, 8][[;; , 2]] (* Harvey P. Dale, Aug 11 2023 *)

Prog

(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A092124(n): return ((1<<(1<<n))+2)*A092124(n-1) if n else 2 # Chai Wah Wu, Nov 23 2023

Crossrefs

Cf. A333447, A367033.

Sequence in context: A165950 A208651 A083667 * A009525 A009683 A132879

Adjacent sequences: A092121 A092122 A092123 * A092125 A092126 A092127

Keyword

nonn

Author

Reinhard Zumkeller, Mar 30 2004

Status

approved