|
%I #35 Jan 07 2019 11:54:00
%S 1,2,4,11,97,3211265
%N Number of nodes in largest rooted identity tree of height n.
%C The next term is 19735 digits long, which is too large even for a b-file.
%C Also, the sequence gives the number of pairs of braces in the n-th iteration of the von Neumann universe. - _Adam P. Goucher_, Aug 18 2013
%H Adam P. Goucher, <a href="http://cp4space.wordpress.com/2013/07/17/von-neumann-universe/">Article including the first five iterations of the von Neumann universe</a>, "Complex Projective 4-Space" blog.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F Recurrence relation: a(n+1) = (a(n) + 1)*(2^^n)/2 + 1 where 2^^n is Knuth's up-arrow notation. - _Adam P. Goucher_, Aug 18 2013
%e For n = 3, the n-th iteration of the von Neumann universe is V3 = {{}, {{}}, {{{}}}, {{},{{}}}}, which has a(3) = 11 pairs of braces.
%p h:= (b, k)-> `if`(k=0, 1, b^h(b, k-1)):
%p a:= proc(n) option remember; `if`(n=0, 1,
%p 1+(1+a(n-1))/2*h(2, n-1))
%p end:
%p seq(a(n), n=0..5); # _Alois P. Heinz_, Aug 25 2017
%t Map[#[[1]]&,NestList[{(#[[1]]+1)*(2^#[[2]])/2+1,2^#[[2]]}&,{1,0},6]] (* _Adam P. Goucher_, Aug 18 2013 *)
%Y Cf. A038082, A038083, A038084, A038085, A038086, A038087, A038088, A038089, A038090, A038091, A038092, A229403, A229404.
%Y Cf. A227819.
%K nonn
%O 0,2
%A _Christian G. Bower_, Jan 04 1999
%E a(6) from _Adam P. Goucher_, Aug 18 2013
|
