

A038093


Number of nodes in largest rooted identity tree of height n.


15




OFFSET

0,2


COMMENTS

The next term is 19735 digits long, which is too large even for a bfile.
Also, the sequence gives the number of pairs of braces in the nth iteration of the von Neumann universe.  Adam P. Goucher, Aug 18 2013


LINKS



FORMULA

Recurrence relation: a(n+1) = (a(n) + 1)*(2^^n)/2 + 1 where 2^^n is Knuth's uparrow notation.  Adam P. Goucher, Aug 18 2013


EXAMPLE

For n = 3, the nth iteration of the von Neumann universe is V3 = {{}, {{}}, {{{}}}, {{},{{}}}}, which has a(3) = 11 pairs of braces.


MAPLE

h:= (b, k)> `if`(k=0, 1, b^h(b, k1)):
a:= proc(n) option remember; `if`(n=0, 1,
1+(1+a(n1))/2*h(2, n1))
end:


MATHEMATICA

Map[#[[1]]&, NestList[{(#[[1]]+1)*(2^#[[2]])/2+1, 2^#[[2]]}&, {1, 0}, 6]] (* Adam P. Goucher, Aug 18 2013 *)


CROSSREFS

Cf. A038082, A038083, A038084, A038085, A038086, A038087, A038088, A038089, A038090, A038091, A038092, A229403, A229404.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



