1,2

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 (rgwv(at)rgwv.com), 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 (njas(AT)research.att.com), 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 (noe(AT)sspectra.com), Jun 22 2007

Eric Weisstein's World of Mathematics, Tribonacci Number

The terms 1, 4, 81, 3136, 10609 are members of the sequence since their square roots are 1, 2, 9, 56, 103 respectively.

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 *)

Cf. A000073.

Sequence in context: A017006 A041189 A123198 this_sequence A068087 A090599 A133396

Adjacent sequences: A128908 A128909 A128910 this_sequence A128912 A128913 A128914

nonn

David Gillies (daggillies(AT)gmail.com), Apr 23 2007

Edited by Robert G. Wilson v (rgwv(at)rgwv.com), Apr 24 2007

More terms from T. D. Noe (noe(AT)sspectra.com), Jun 22 2007