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

0, 0, 1, 2, 4, 7, 0, 3, 10, 26, 60, 130, 38, 173, 485, 175, 977, 273, 2789, 2065, 336, 15149, 22718, 39800, 5226, 54214, 2323, 251416, 418400, 93831, 977776, 1518664, 261912, 5208104, 2557037, 3549042, 21177270, 11203146, 36247269, 87596844, 44950918, 261069681

Offset: 1

Author

Richard Peterson, Jun 12 2020

Keywords

• nonn

Comments

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

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000

Crossrefs

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

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|1|1>>^n)[1, 3] mod (<<0|1>, <1|1>>^n)[1, 2]:
seq(a(n), n=1..45);  # Alois P. Heinz, Aug 19 2020

Mathematica

m = 42; Mod[LinearRecurrence[{1, 1, 1}, {0, 1, 1}, m], Array[Fibonacci, m]] (* Amiram Eldar, Aug 19 2020 *)

PARI

t(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073
a(n) = t(n) % fibonacci(n); \\ Michel Marcus, Aug 19 2020