# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a020992 Showing 1-1 of 1 %I A020992 #41 Sep 08 2022 08:44:45 %S A020992 0,2,1,3,6,10,19,35,64,118,217,399,734,1350,2483,4567,8400,15450, %T A020992 28417,52267,96134,176818,325219,598171,1100208,2023598,3721977, %U A020992 6845783,12591358,23159118,42596259,78346735,144102112,265045106,487493953,896641171,1649180230 %N A020992 a(n) = a(n-1) + a(n-2) + a(n-3). %C A020992 Tribonacci sequence beginning 0, 2, 1. %C A020992 Pisano period lengths: 1, 4, 13, 8, 31, 52, 48, 16, 39, 124, 110, 104, 168, 48, 403, 32, 96, 156, 360, 248,.... - _R. J. Mathar_, Aug 10 2012 %C A020992 One bisection is 0, 1, 6, 19, 64, 217, 734, 2483, 8400,.. and the other 2, 3, 10, 35, 118, 399, 1350, 4567,... both with recurrence b(n)=3*b(n-1)+b(n-2)+b(n-3). - _R. J. Mathar_, Aug 10 2012 %H A020992 Robert Price, Table of n, a(n) for n = 0..1000 %H A020992 Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. %H A020992 Index entries for linear recurrences with constant coefficients, signature (1,1,1). %F A020992 G.f.: x*(2-x)/(1-x-x^2-x^3). %F A020992 a(n) = 2*A000073(n+1)-A000073(n). - _R. J. Mathar_, Aug 22 2008 %F A020992 a(n) = 2*a(n-1) - a(n-4), n>3. - _Vincenzo Librandi_, Jun 08 2011 %t A020992 LinearRecurrence[{1,1,1},{0,2,1},100] (* _Vladimir Joseph Stephan Orlovsky_, Jun 07 2011 *) %o A020992 (PARI) x='x+O('x^30); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ _G. C. Greubel_, Feb 09 2018 %o A020992 (Magma) I:=[0,2,1]; [n le 3 select I[n] else Self(n-1) + Self(n-2) + Self(n-3): n in [1..30]]; // _G. C. Greubel_, Feb 09 2018 %Y A020992 Cf. A000032, A000073, A001590, A232498, A233554. %K A020992 nonn,easy %O A020992 0,2 %A A020992 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE