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

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Peter Cameron, A little problem, May 31 2021.

Volkan Yildiz, Some divisibility properties of Jacobsthal numbers, arXiv:2212.08814 [math.CO], 2022.

Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Formula

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

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

G.f.: (1 - 2*x + 16*x^2)/((1 - x)*(1 - 4*x)*(1 - 16*x)). - Andrew Howroyd, Nov 11 2025

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 *)

Prog

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

Crossrefs

Cf. A002061, A004171.

Sequence in context: A014900 A121324 A093973 * A202043 A142549 A049629

Adjacent sequences: A345960 A345961 A345962 * A345964 A345965 A345966

Keyword

nonn,easy

Author

Michel Marcus, Jun 30 2021

Status

approved