Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Mar 03 2024 14:43:36
%S 1,2,19,188,1861,18422,182359,1805168,17869321,176888042,1751011099,
%T 17333222948,171581218381,1698478960862,16813208390239,
%U 166433604941528,1647522841025041,16308794805308882,161440425212063779,1598095457315328908,15819514147941225301
%N a(n) = 10*a(n-1) - a(n-2).
%C A140780 has the same recursion rule but starts (1, 3, 29,...).
%C a(n)/a(n-1) tends to 2*sqrt(6) + 5 = 9.8989794855...
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -1).
%F a(n) = 10*a(n-1) - a(n-2); n>1; given a(0) = 1, a(1) = 2. a(n) = term (1,1) in X^n, where X = the 2x2 matrix [2,3; 5,8].
%e a(5) = 18422 = 10*a(4) - a(3) = 10*1861 - 188.
%e a(3) = 188 = term (1,1) of X^3.
%t LinearRecurrence[{10, -1}, {1, 2}, 30] (* _Amiram Eldar_, Dec 04 2018 *)
%Y Cf. A140780.
%K nonn
%O 0,2
%A _Gary W. Adamson_, May 30 2008
%E More terms from _Amiram Eldar_, Dec 04 2018