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A092124 a(0) = 2, a(n) = (2^(2^n)+2)*a(n-1) for n>0. 2
2, 12, 216, 55728, 3652301664, 15686516209310983872, 289365149921256212111714425927549504896, 98465858119637274097902770931519409290135390781788892125023848289699334298368 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..7.

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 *)

CROSSREFS

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

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)