OFFSET
1,3
COMMENTS
These are the only square tribonacci numbers having indices < 47000.
Next term, if it exists, is too large to present here. - Robert G. Wilson v, Apr 24 2007
Indices of the square tribonacci numbers: 1,4,9,15,17.
The square Fibonacci numbers seem to be even rarer, namely just 1 & 144. - Robert G. Wilson v, Apr 24 2007
It is very likely that there are no further terms. - N. J. A. Sloane, Apr 25 2007
Using modular arithmetic and quadratic residues, it can be shown that there are no additional squares in the first 10^9 tribonacci numbers. - T. D. Noe, Jun 22 2007
LINKS
Attila Pethö, Fifteen problems in number theory, Acta Universitatis Sapientiae. Mathematica (2010) Volume: 2, Issue: 1, page 72-83. See Problem 1.
Eric Weisstein's World of Mathematics, Tribonacci Number
EXAMPLE
The terms 0, 1, 4, 81, 3136, 10609 are members of the sequence since their square roots are 0, 1, 2, 9, 56, 103 respectively.
MATHEMATICA
a = b = 0; c = 1; lst = {}; Do[{a, b, c} = {b, c, a + b + c}; If[ IntegerQ@ Sqrt@c, AppendTo[lst, c]], {n, 2, 47000}]; lst (* Robert G. Wilson v, Apr 24 2007 *)
Drop[Select[LinearRecurrence[{1, 1, 1}, {0, 1, 1}, 20], IntegerQ[Sqrt[#]]&], 2] (* Harvey P. Dale, Mar 17 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David A. G. Gillies, Apr 23 2007
EXTENSIONS
Edited by Robert G. Wilson v, Apr 24 2007
More terms from T. D. Noe, Jun 22 2007
a(1) = 0 inserted by Felix Fröhlich, Dec 11 2019
STATUS
approved