A380083 a(n) = Pell(n^2)/Pell(n).

1, 6, 197, 39236, 45232349, 304285766994, 11928254138546089, 2725453049877127789064, 3629520789795568149638626009, 28171611459441395148628640333550174, 1274457582507820938168220698796661580252461, 336039604487720392926819615640785342048933644491212

Offset: 1

Author

Seiichi Manyama, May 08 2025

Keywords

• nonn
• easy

Crossrefs

Main diagonal of A383742.

Cf. A000129, A002203, A051294, A204327.

Programs

Maple

a:= n-> (f->f(n^2)/f(n))(k->(<<2|1>, <1|0>>^k)[1, 2]):
seq(a(n), n=1..12);  # Alois P. Heinz, May 08 2025

Mathematica

a[n_] := Fibonacci[n^2, 2]/Fibonacci[n, 2]; Array[a, 12] (* Amiram Eldar, May 08 2025 *)

PARI

pell(n) = ([2, 1; 1, 0]^n)[2, 1];
a(n) = pell(n^2)/pell(n);

Formula

a(n) = A204327(n)/A000129(n).

a(n) = [x^n] x/(1 - A002203(n)*x + (-1)^n*x^2).