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%I #41 Jun 10 2022 06:16:46
%S 0,1,2,9,56,103
%N Integers whose squares are in A000073 (tribonacci numbers).
%C a(6) > 10^7. - _Tom Edgar_, Apr 26 2014
%C Is this sequence finite?
%C No more terms < 10^19300. I conjecture that the sequence is finite. - _Manfred Scheucher_, Aug 17 2015
%e 9^2 = 81 is in the tribonacci sequence, so 9 is a term.
%t Select[Sqrt[#]&/@LinearRecurrence[{1,1,1},{0,0,1},200],IntegerQ]// Union (* _Harvey P. Dale_, Aug 16 2021 *)
%o (Sage)
%o def tribs():
%o a,b,c = 0,0,1
%o while True:
%o yield a
%o a,b,c = b,c,a+b+c
%o for n in tribs():
%o m = sqrt(n)
%o if m.is_integer():
%o print(m) # _Manfred Scheucher_, Aug 17 2015
%Y Cf. A000073 (tribonacci numbers), A128911 (the corresponding squares).
%K nonn,more,hard
%O 1,3
%A _J. Lowell_, Apr 16 2014
%E Zero prepended by _Harvey P. Dale_, Aug 16 2021