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A350253
a(n) = A000045(n)^A000045(n+1) mod A000045(n+2).
2
0, 1, 1, 3, 3, 1, 8, 13, 1, 55, 55, 1, 144, 233, 1, 987, 987, 1, 2584, 4181, 1, 17711, 17711, 1, 46368, 75025, 1, 317811, 317811, 1, 832040, 1346269, 1, 5702887, 5702887, 1, 14930352, 24157817, 1, 102334155, 102334155, 1, 267914296, 433494437, 1, 1836311903, 1836311903, 1, 4807526976, 7778742049
OFFSET
0,4
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,18,0,0,-18,0,0,-1,0,0,1).
FORMULA
a(n) = 1 if n == 2 or 5 (mod 6),
= A000045(n) if n == 0, 1 or 4 (mod 6),
= A000045(n+1) if n == 3 (mod 6).
G.f.: (z + z^2 + 3*z^3 + 2*z^4 + 5*z^6 - 8*z^7 - 18*z^8 - 7*z^9 + 6*z^10 - z^12 - z^13 + z^14)/(1 - z^3 - 18*z^6 + 18*z^9 + z^12 - z^15).
EXAMPLE
a(3) = 2^3 mod 5 = 3.
MAPLE
f:= proc(n)
if n mod 6 = 3 then combinat:-fibonacci(n+1)
elif n mod 3 = 2 then 1
else combinat:-fibonacci(n)
fi
end proc:
map(f, [$0..100]);
MATHEMATICA
Table[PowerMod @@ Fibonacci[n + {0, 1, 2}], {n, 0, 50}] (* Amiram Eldar, Dec 22 2021 *)
PROG
(PARI) a(n) = lift(Mod(fibonacci(n), fibonacci(n+2))^fibonacci(n+1)); \\ Michel Marcus, Dec 22 2021
(Python)
from sympy import fibonacci
def A350253(n): return 1 if (m := n % 6) == 2 or m == 5 else (fibonacci(n+1) if m == 3 else fibonacci(n)) # from formula Chai Wah Wu, Dec 22 2021
CROSSREFS
Cf. A000045.
Sequence in context: A293294 A200342 A181330 * A262143 A284554 A078033
KEYWORD
nonn,easy
AUTHOR
J. M. Bergot and Robert Israel, Dec 21 2021
STATUS
approved