A345963 a(n) = (q^2-q+1)/3 where q = 2^(2*n+1) = A004171(n).

1, 19, 331, 5419, 87211, 1397419, 22366891, 357903019, 5726579371, 91625794219, 1466014804651, 23456245263019, 375299957762731, 6004799458421419, 96076791871613611, 1537228672093301419, 24595658762082757291, 393530540227683855019, 6296488643780380633771, 100743818301035845954219

Offset: 0

Author

Michel Marcus, Jun 30 2021

Keywords

• nonn

Links

• Peter Cameron, A little problem, May 31 2021.
• Volkan Yildiz, Some divisibility properties of Jacobsthal numbers, arXiv:2212.08814 [math.CO], 2022.

Crossrefs

Cf. A002061, A004171.

Programs

Maple

a:= n-> (q-> (q^2-q+1)/3)(2^(2*n+1)):
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 30 2021

Mathematica

Table[(2^(4*n + 2) - 2^(2*n + 1) + 1)/3, {n, 0, 19}] (* Amiram Eldar, Jun 30 2021 *)

PARI

a(n) = my(q=2^(2*n+1)); (q^2-q+1)/3;

Formula

a(n) = A002061(A004171(n))/3.

a(n) = (A060869(n) + 1)/4. - Hugo Pfoertner, Jun 30 2021