A395582 - OEIS

%I #15 May 05 2026 00:39:15

%S 0,1,3,12,48,197,808,3318,13626,55961,229829,943899,3876559,15920890,

%T 65386531,268540168,1102884965,4529509517,18602535276,76399953992,

%U 313771907077,1288650117266,5292440423364,21735865507300,89268430356963,366622284064081,1505704745058057

%N a(n) = floor(r*a(n-1)) + floor(r*a(n-2)), a(0) = 0, a(1) = 1 and r = (3 + sqrt(13))/2.

%C r is the bronze ratio A098316.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-2,-1,-1).

%F Limit_{n -> oo} a(n)/a(n-1) = A395592.

%F a(n) = A080081(a(n-1)) + A080081(a(n-2)).

%t LinearRecurrence[{4, 1, -2, -1, -1}, {0, 1, 3, 12, 48}, 27] (* _Amiram Eldar_, May 02 2026 *)

%Y Cf. A080081, A098316, A395592.

%Y Cf. A005908, A272362, A274203, A395581, A395583, A395585, A395586.

%K nonn,easy

%O 0,3

%A _A.H.M. Smeets_, Apr 29 2026