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A318053 a(n) = ceiling(sqrt(2*a(n-1)*a(n-2))), a(1) = a(2) = 1.

%I A318053 #20 Apr 13 2020 12:05:37
%S A318053 1,1,2,2,3,4,5,7,9,12,15,19,24,31,39,50,63,80,101,128,161,204,257,324,
%T A318053 409,515,650,819,1032,1301,1639,2066,2603,3280,4133,5207,6561,8266,
%U A318053 10415,13122,16533,20831,26245,33067,41662,52491,66135,83325
%N A318053 a(n) = ceiling(sqrt(2*a(n-1)*a(n-2))), a(1) = a(2) = 1.
%C A318053 a(n)/a(n-1) ~ cube root of 2.
%C A318053 a(n)/a(n-3) ~ 2.
%e A318053 a(12) = ceiling(sqrt(2*a(11)*a(10))) = ceiling(sqrt(2*15*12)) = ceiling(sqrt(360)) = 19.
%t A318053 a[n_] := a[n] = If[n<3, 1, Ceiling[Sqrt[2 a[n-1] a[n-2]]]]; Array[a, 50] (* _Giovanni Resta_, Nov 26 2019 *)
%t A318053 RecurrenceTable[{a[1]==a[2]==1,a[n]==Ceiling[Sqrt[2a[n-1]a[n-2]]]},a,{n,50}] (* _Harvey P. Dale_, Apr 13 2020 *)
%o A318053 (Python)
%o A318053 import math
%o A318053 r = []
%o A318053 r.append(1)
%o A318053 r.append(1)
%o A318053 i = 2
%o A318053 while i < 1001:
%o A318053   r.append(math.ceil(math.sqrt(2*r[i-1]*r[i-2])))
%o A318053   i += 1
%o A318053 print(r)
%Y A318053 Cf. A017981.
%K A318053 nonn
%O A318053 1,3
%A A318053 _Oren Meisner_, Aug 14 2018