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%I #28 Mar 16 2024 15:20:45
%S 1,4,9,14,27,50,91,168,309,568,1045,1922,3535,6502,11959,21996,40457,
%T 74412,136865,251734,463011,851610,1566355,2880976,5298941,9746272,
%U 17926189,32971402,60643863,111541454,205156719,377342036,694040209
%N Tribonacci numbers that start with first three squares.
%C n and a(n) are of the same parity. Except for the first three terms and a(5)=27, there is no perfect powers (A001597) in the first 225 terms. In fact there is always at least one factor which is represented only once. - _Robert G. Wilson v_, Aug 27 2003
%H Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.pdf">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F a(n) = a(n-1) + a(n-2) + a(n-3).
%F From _R. J. Mathar_, Apr 20 2009: (Start(
%F a(n) = 4*A000073(n) + 3*A000073(n-1) + A000073(n-2).
%F G.f.: -x*(1+3*x+4*x^2)/(-1+x+x^2+x^3). (End)
%t a[1] = 1; a[2] = 4; a[3] = 9; a[n_] := a[n] = a[n - 3] + a[n - 2] + a[n - 1]; Table[ a[n], {n, 1, 30}]
%t Transpose[NestList[Flatten[{Rest[#],Total[#]}]&,{1,4,9},40]][[1]] (* _Harvey P. Dale_, Mar 24 2011 *)
%t LinearRecurrence[{1,1,1},{1,4,9},33] (* _Ray Chandler_, Dec 08 2013 *)
%Y Cf. A000073, A000213, A001597.
%K nonn,easy
%O 1,2
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 26 2003
%E More terms from _Robert G. Wilson v_, Aug 27 2003
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