A396358 a(n) = J((n-1)*(n+1))/(J(n-1)*J(n+1)), where J(n) is the n-th Jacobsthal number A001045(n).

1, 2, 1, 17, 331, 53261, 24214051, 52563020861, 418122854021251, 13902890226147193085, 1808970572192153926885891, 951899710171488635310071333885, 1992625672714809319380748222257399811, 16730664443183919857072575998454953999798269, 561131004848296743814407155757684273574228050976771

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..58

Formula

a(n) = J((n-1)*(n+1))/(J(n-1)*J(n+1)) with J(n) = ((1+sqrt(9))^n - (1-sqrt(9))^n)/(2^n*sqrt(9)). a(1) = 2 is found by taking the limit of the quotient for n->1.

a(n) mod 3 = A000034(n).

a(n) mod 2 = A060576(n).

Maple

J:= n-> ((1+sqrt(9))^n-(1-sqrt(9))^n)/(2^n*sqrt(9)):
a:= n-> `if`(n=1, 2, J((n-1)*(n+1))/(J(n-1)*J(n+1))):
seq(a(n), n=0..14);

Crossrefs

Cf. A000034, A001045, A060576, A378676, A396115, A396233.

Sequence in context: A013072 A012895 A013077 * A225768 A335024 A270927

Adjacent sequences: A396355 A396356 A396357 * A396359 A396360 A396361

Keyword

nonn,easy

Author

Alois P. Heinz, May 23 2026

Status

approved