A205505 a(n) = Fibonacci(n*(n+1)) / Fibonacci(n).

1, 8, 72, 2255, 166408, 33489287, 17373187209, 23735905327584, 84707858657965180, 792123204706451722511, 19386236394149894806708656, 1242293991563772001787883943693, 208405704482555536994509895576090977, 91533085042008706066658193727853843719640

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..69

Formula

a(n) = [x^n] 1/(1 - Lucas(n)*x + (-1)^n*x^2), where Lucas(n) = A000204(n).

Forms a diagonal in table A028412.

Maple

a:= n-> (f->f(n*(n+1))/f(n))(k->(<<0|1>, <1|1>>^k)[1, 2]):
seq(a(n), n=1..14);  # Alois P. Heinz, May 17 2026

Mathematica

Table[Fibonacci[n(n+1)]/Fibonacci[n], {n, 20}] (* Harvey P. Dale, Mar 30 2012 *)

Prog

(PARI) {a(n)=fibonacci(n*(n+1))/fibonacci(n)}
(PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
{a(n)=polcoeff(1/(1-Lucas(n)*x+(-1)^n*x^2+x*O(x^n)), n)}

Crossrefs

Cf. A000045, A103624, A051294, A028412.

Sequence in context: A339469 A241032 A001799 * A058068 A096873 A282786

Adjacent sequences: A205502 A205503 A205504 * A205506 A205507 A205508

Keyword

nonn,easy

Author

Paul D. Hanna, Jan 28 2012

Status

approved