A396358 - OEIS

%I #14 May 27 2026 20:05:09

%S 1,2,1,17,331,53261,24214051,52563020861,418122854021251,

%T 13902890226147193085,1808970572192153926885891,

%U 951899710171488635310071333885,1992625672714809319380748222257399811,16730664443183919857072575998454953999798269,561131004848296743814407155757684273574228050976771

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

%H Alois P. Heinz, <a href="/A396358/b396358.txt">Table of n, a(n) for n = 0..58</a>

%F 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.

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

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

%p J:= n-> ((1+sqrt(9))^n-(1-sqrt(9))^n)/(2^n*sqrt(9)):

%p a:= n-> `if`(n=1, 2, J((n-1)*(n+1))/(J(n-1)*J(n+1))):

%p seq(a(n), n=0..14);

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

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, May 23 2026