A332409 a(n) = n!! mod Fibonacci(n).

0, 0, 1, 2, 0, 0, 1, 6, 27, 45, 71, 0, 228, 73, 605, 861, 956, 2376, 1199, 5235, 7137, 5017, 21617, 40320, 49250, 72900, 94129, 253071, 125204, 188760, 786046, 1041600, 3306329, 2717231, 8692580, 4869072, 10661888, 33618132, 14333453, 66880275, 110783982

Offset

1,4

Comments

a(n) = 0 for n = 1, 2, 5, 6, 12 (a(n) < 500).

Links

Table of n, a(n) for n=1..41.

Formula

a(n) = n!! mod Fibonacci(n).

where n!! denotes the double factorial of n (n!! = n*a(n-2) for n > 1, a(0) = a(1) = 1), and Fibonacci(n) denotes the n-th Fibonacci number.

Example

For n = 1, a(1) = 1!! mod Fibonacci(1) = 1 mod 1 = 0.
For n = 4, a(4) = 4!! mod Fibonacci(4) = 8 mod 3 = 2.

Mathematica

Table[Mod[n!!, Fibonacci[n]], {n, 50}] (* Harvey P. Dale, Sep 08 2020 *)

Prog

(PARI) a0(n) = my(f=fibonacci(n)); prod(i=0, (n-1)\2, n - 2*i) % f; \\ Michel Marcus, Mar 17 2020

Crossrefs

Cf. A000045, A006882, A182213.

Sequence in context: A127826 A228866 A109983 * A367000 A289084 A193033

Adjacent sequences: A332406 A332407 A332408 * A332410 A332411 A332412

Keyword

nonn,easy

Author

Andrew Nelson, Feb 17 2020

Status

approved