A343575 a(n) = floor((2+sqrt(5))^n - 2^(n+1)) mod (20*n).

0, 9, 0, 49, 0, 9, 0, 129, 60, 49, 0, 49, 0, 9, 100, 129, 0, 249, 0, 49, 340, 9, 0, 449, 0, 9, 240, 289, 0, 249, 0, 129, 60, 9, 600, 49, 0, 9, 580, 449, 0, 609, 0, 289, 700, 9, 0, 449, 700, 249, 60, 289, 0, 969, 200, 129, 60, 9, 0, 49, 0, 9, 1240, 769, 0, 369, 0

Offset: 1

Author

William C. Laursen, Apr 20 2021

Keywords

• nonn
• easy

Comments

Whenever n is an odd prime, a(n) is 0 (see M. Penn).

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• M. Penn, Hello, old friend..., YouTube video.

Crossrefs

Cf. A345031.

Programs

Mathematica

Table[Mod[Floor[(2+Sqrt[5])^n-2^(n+1)],20n],{n,67}] (* Stefano Spezia, Apr 21 2021 *)

PARI

a(n) = my(M = [6, -7, -2; 1, 0, 0; 0, 1, 0]); 10*((M^n)[3, 1] % (2*n)) - !(n%2) \\ Jianing Song, Jun 07 2021

Formula

From Jianing Song, Jun 07 2021: (Start)

For even n, a(n) = 10*(A345031(n) mod (2*n)) - 1;

For odd n, a(n) = 10*(A345031(n) mod (2*n)). (End)

Extensions

More terms from Stefano Spezia, Apr 21 2021