cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A335534 a(n) = tribonacci(n) modulo Fibonacci(n).

This page as a plain text file.
%I A335534 #34 Jul 21 2021 09:33:19
%S A335534 0,0,1,2,4,7,0,3,10,26,60,130,38,173,485,175,977,273,2789,2065,336,
%T A335534 15149,22718,39800,5226,54214,2323,251416,418400,93831,977776,1518664,
%U A335534 261912,5208104,2557037,3549042,21177270,11203146,36247269,87596844,44950918,261069681
%N A335534 a(n) = tribonacci(n) modulo Fibonacci(n).
%C A335534 a(n) is congruent to tribonacci(n) modulo k if Fibonacci(n) is divisible by k, although the converse does not hold.
%H A335534 Alois P. Heinz, <a href="/A335534/b335534.txt">Table of n, a(n) for n = 1..2000</a>
%e A335534 For n=10, since tribonacci(10)=81 and Fibonacci(10)=55, a(10)=81 modulo 55 = 26.
%p A335534 a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^n)[1, 3] mod (<<0|1>, <1|1>>^n)[1, 2]:
%p A335534 seq(a(n), n=1..45);  # _Alois P. Heinz_, Aug 19 2020
%t A335534 m = 42; Mod[LinearRecurrence[{1, 1, 1}, {0, 1, 1}, m], Array[Fibonacci, m]] (* _Amiram Eldar_, Aug 19 2020 *)
%o A335534 (PARI) t(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073
%o A335534 a(n) = t(n) % fibonacci(n); \\ _Michel Marcus_, Aug 19 2020
%Y A335534 Cf. A000073, A000045, A001177, A133021, A046738.
%K A335534 nonn
%O A335534 1,4
%A A335534 _Richard Peterson_, Jun 12 2020