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

1,4

Comments

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

Links

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

Example

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

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 *)
With[{nn=50}, {trib=LinearRecurrence[{1, 1, 1}, {0, 1, 1}, nn]}, Mod[#[[1]], #[[2]]]&/@Thread[{trib, Fibonacci[Range[nn]]}]] (* Harvey P. Dale, Dec 20 2025 *)

Prog

(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

Crossrefs

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

Sequence in context: A283509 A111768 A011177 * A213673 A118946 A097879

Adjacent sequences: A335531 A335532 A335533 * A335535 A335536 A335537

Keyword

nonn

Author

Richard Peterson, Jun 12 2020

Status

approved