cp's OEIS Frontend

A280308 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=3, a(1)=4, a(2)=5.

%I A280308 #23 Jan 19 2019 04:15:43
%S A280308 3,4,5,12,21,38,71,130,239,440,809,1488,2737,5034,9259,17030,31323,
%T A280308 57612,105965,194900,358477,659342,1212719,2230538,4102599,7545856,
%U A280308 13878993,25527448,46952297,86358738,158838483,292149518,537346739,988334740,1817830997,3343512476,6149678213,11311021686,20804212375
%N A280308 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=3, a(1)=4, a(2)=5.
%C A280308 Like other tribonacci sequences, the digital root is period length 39, and is as follows: (3, 4, 5, 3, 3, 2, 8, 4, 5, 8, 8, 3, 1, 3, 7, 2, 3, 3, 8, 5, 7, 2, 5, 5, 3, 4, 3, 1, 8, 3, 3, 5, 2, 1, 8, 2, 2, 3, 7).
%C A280308 Completes the set of tribonacci numbers with 3,4,5 as initial terms, the others being (3,5,4), (4,5,3), (4,3,5), (5,3,4), and (5,4,3). The sum of each of the digital root periods in the above set is 162, except (4,3,5), which sums to 180; the sum of the digital root period of A081172 is also 180.
%C A280308 Each digital root period for tribonacci sequences has triple patterns in cycles of 13, such as period (1,4,7) or digital root of 4^n.
%H A280308 Vincenzo Librandi, <a href="/A280308/b280308.txt">Table of n, a(n) for n = 0..1000</a>
%H A280308 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A280308 G.f.: (3+x-2*x^2)/(1-x-x^2-x^3). - _Vincenzo Librandi_, Jan 01 2017
%t A280308 RecurrenceTable[{a[n] == a[n - 1] + a[n - 2] + a[n - 3], a[0] == 3, a[1] == 4, a[2] == 5}, a, {n, 38}] (* _Michael De Vlieger_, Dec 31 2016 *)
%t A280308 LinearRecurrence[{1, 1, 1}, {3, 4, 5}, 40] (* _Vincenzo Librandi_, Jan 01 2017 *)
%Y A280308 Cf. A000073, A001590, A081172, A000213.
%K A280308 nonn,easy
%O A280308 0,1
%A A280308 _Peter M. Chema_, Dec 31 2016