A348592 a(n) = F(n)*F(n+1) mod L(n+2) where F=A000045 is the Fibonacci numbers and L = A000032 is the Lucas numbers.
0, 1, 2, 6, 15, 11, 10, 45, 99, 79, 65, 312, 675, 545, 442, 2142, 4623, 3739, 3026, 14685, 31683, 25631, 20737, 100656, 217155, 175681, 142130, 689910, 1488399, 1204139, 974170, 4728717, 10201635, 8253295, 6677057, 32411112, 69923043, 56568929, 45765226, 222149070, 479259663, 387729211, 313679522
Offset: 0
Examples
a(5) = F(5)*F(6) mod L(7) = 5*8 mod 29 = 11.
Links
- Robert Israel, Table of n, a(n) for n = 0..4759
- Index entries for linear recurrences with constant coefficients, signature (0,-1,1,5,3,2,1).
Programs
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Maple
F:= combinat:-fibonacci: L:= n -> F(n-1)+F(n+1): seq(F(n)*F(n+1) mod L(n+2), n=0..20);
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Mathematica
a[n_] := Mod[Fibonacci[n] * Fibonacci[n + 1], LucasL[n + 2]]; Array[a, 50, 0] (* Amiram Eldar, Jan 26 2022 *)