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A128911
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Square tribonacci numbers.
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0
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OFFSET
| 1,2
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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 (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
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LINKS
| Eric Weisstein's World of Mathematics, Tribonacci Number
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EXAMPLE
| The terms 1, 4, 81, 3136, 10609 are members of the sequence since their square roots are 1, 2, 9, 56, 103 respectively.
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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 *)
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CROSSREFS
| Cf. A000073.
Sequence in context: A041189 A123198 A202831 * A068087 A090599 A133396
Adjacent sequences: A128908 A128909 A128910 * A128912 A128913 A128914
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KEYWORD
| nonn
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AUTHOR
| David Gillies (daggillies(AT)gmail.com), Apr 23 2007
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EXTENSIONS
| 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
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