A335534 - OEIS

%I #34 Jul 21 2021 09:33:19

%S 0,0,1,2,4,7,0,3,10,26,60,130,38,173,485,175,977,273,2789,2065,336,

%T 15149,22718,39800,5226,54214,2323,251416,418400,93831,977776,1518664,

%U 261912,5208104,2557037,3549042,21177270,11203146,36247269,87596844,44950918,261069681

%N a(n) = tribonacci(n) modulo Fibonacci(n).

%C a(n) is congruent to tribonacci(n) modulo k if Fibonacci(n) is divisible by k, although the converse does not hold.

%H Alois P. Heinz, <a href="/A335534/b335534.txt">Table of n, a(n) for n = 1..2000</a>

%e For n=10, since tribonacci(10)=81 and Fibonacci(10)=55, a(10)=81 modulo 55 = 26.

%p a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^n)[1, 3] mod (<<0|1>, <1|1>>^n)[1, 2]:

%p seq(a(n), n=1..45);  # _Alois P. Heinz_, Aug 19 2020

%t m = 42; Mod[LinearRecurrence[{1, 1, 1}, {0, 1, 1}, m], Array[Fibonacci, m]] (* _Amiram Eldar_, Aug 19 2020 *)

%o (PARI) t(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073

%o a(n) = t(n) % fibonacci(n); \\ _Michel Marcus_, Aug 19 2020

%Y Cf. A000073, A000045, A001177, A133021, A046738.

%K nonn

%O 1,4

%A _Richard Peterson_, Jun 12 2020