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%I #24 May 30 2020 15:43:07
%S 1,4,9,16,36,81,169,324,676,1369,2704,5476,11025,21904,44100,88209,
%T 176400,352836,705600,1411344,2822400,5645376,11296321,22591009,
%U 45185284,90364036,180741136,361494169,722964544,1445976676,2891965729
%N a(1) = 1, a(n+1) is the smallest square greater than the n-th partial sum.
%C Lim_{n->infinity} a(n)/(2^n) = 1.34669079829214755988545564864530863502076381405786.... - _Jon E. Schoenfield_, Oct 04 2013
%H Nathaniel Johnston, <a href="/A076967/b076967.txt">Table of n, a(n) for n = 1..1000</a>
%F Lim_{n->infinity} a(n+1)/a(n) = 2. - _Zak Seidov_, May 03 2009
%e a(5) = 36 because it is the smallest square greater than the sum of a(1)..a(4) = 30.
%p a[1] := 1:a[2] := 4:for n from 3 to 45 do a[n] := ceil(evalf(sqrt(sum(a[i],i=1..n-1)+1/10^19),100))^2; od:seq(a[k],k=1..45);
%t nxt[{p_,a_}]:=Module[{k=1},While[!IntegerQ[Sqrt[p+k]],k++];{2p+k,p+k}]; NestList[nxt,{1,1},30][[All,2]] (* _Harvey P. Dale_, May 30 2020 *)
%Y Cf. A076968.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Oct 21 2002
%E Corrected and extended by _Sascha Kurz_, Jan 22 2003
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