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A174864 a(1) = 1, a(n) = square of the sum of previous terms. 5
1, 1, 4, 36, 1764, 3261636, 10650053687364, 113423713055411194304049636, 12864938683278671740537145884937248491231415124195364 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..13

Index entries for sequences of form a(n+1)=a(n)^2 + ...

FORMULA

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

a(n+1) = (a(n) + sqrt(a(n)))^2 = a(n) * (sqrt(a(n)) + 1)^2 for n > 1. [Charles R Greathouse IV, Jun 30 2011]

a(n) = A000058(n-1) - A000058(n-2), n>=2. - Ivan N. Ianakiev, Oct 09 2013

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(100); [Paolo P. Lava, Apr 23 2010]

MATHEMATICA

t = {1}; Do[AppendTo[t, Total[t]^2], {n, 9}]; t (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *)

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[n-1]*(sqrtint(a[n-1])+1)^2); a

CROSSREFS

Cf. A000058, A007018.

Sequence in context: A143764 A152287 A086857 * A175493 A179870 A001152

Adjacent sequences:  A174861 A174862 A174863 * A174865 A174866 A174867

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Mar 31 2010

STATUS

approved

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Last modified February 23 04:57 EST 2018. Contains 299473 sequences. (Running on oeis4.)