

A174864


a(1) = 1, a(n) = square of the sum of previous terms.


5




OFFSET

1,3


COMMENTS

a(n) divides a(n+1) with result a square.
Except for first two terms, partial sum k of a(n) is divisible by 6.
These numbers are divisible by their digital roots, which makes the sequence a subsequence of A064807.  Ivan N. Ianakiev, Oct 09 2013
a(n) is the number of binary trees in which the nodes are labeled by nonnegative integer heights, the left and right children of each node (if present) must have smaller height, and the root has height n2. For instance, there are four trees with root height 1: the left and right children of the root may or may not be present, and must each be at height 0 if present.  David Eppstein, Oct 25 2018


LINKS



FORMULA

a(n+1) = [Sum_{i=1..n}{a(i)}]^2, with a(1)=1.  Paolo P. Lava, Apr 23 2010


MAPLE

P:=proc(i) local a, s, n; a:=1; print(1); s:=1; for n from 0 by 1 to i do a:=s^2; print(a); s:=s+a; od; end: P(10); # Paolo P. Lava, Apr 23 2010


MATHEMATICA

Join[{1}, FoldList[(#+Sqrt[#])^2&, 1, Range[7]]] (* Ivan N. Ianakiev, May 08 2015 *)


PROG

(PARI) a=vector(10); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n1]*(sqrtint(a[n1])+1)^2); a


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



