A347861 a(n) = A000032(n)*A000032(n+1) mod A000032(n+2).

2, 3, 5, 6, 5, 24, 5, 71, 5, 194, 5, 516, 5, 1359, 5, 3566, 5, 9344, 5, 24471, 5, 64074, 5, 167756, 5, 439199, 5, 1149846, 5, 3010344, 5, 7881191, 5, 20633234, 5, 54018516, 5, 141422319, 5, 370248446, 5, 969323024, 5, 2537720631, 5, 6643838874, 5, 17393795996, 5, 45537549119, 5, 119218851366, 5

Offset

0,1

Comments

The analogous sequence for Fibonacci numbers instead of Lucas numbers is A333599.

Links

Robert Israel, Table of n, a(n) for n = 0..4760

Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-1,-1).

Formula

G.f.: 4*x - 3 - (x + 3)/(2*(x^2 + x - 1)) - (x - 3)/(2*(x^2 - x - 1)) + 5/(x + 1).

a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) - a(n-4) - a(n-5) for n >= 7.

a(n) = 5 for even n >= 2.

a(n) = A000032(n+2)-5 for odd n >= 3.

Example

a(3) = A000032(3)*A000032(4) mod A000032(5) = 4*7 mod 11 = 6.

Maple

L:= n -> combinat:-fibonacci(n-1)+combinat:-fibonacci(n+1):
f:= n -> L(n)*L(n+1) mod L(n+2):
map(f, [$0..40]);

Mathematica

With[{L = LucasL}, Table[Mod[L[n]*L[n + 1], L[n + 2]], {n, 0, 50}]] (* Amiram Eldar, Jan 24 2022 *)

Prog

(PARI) L(n) = fibonacci(n+1)+fibonacci(n-1);
a(n) = L(n)*L(n+1) % L(n+2); \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A000032, A333599.

Sequence in context: A247548 A001600 A175578 * A316609 A307327 A000036

Adjacent sequences: A347858 A347859 A347860 * A347862 A347863 A347864

Keyword

nonn,easy

Author

J. M. Bergot and Robert Israel, Jan 23 2022

Status

approved