A395582 a(n) = floor(r*a(n-1)) + floor(r*a(n-2)), a(0) = 0, a(1) = 1 and r = (3 + sqrt(13))/2.

0, 1, 3, 12, 48, 197, 808, 3318, 13626, 55961, 229829, 943899, 3876559, 15920890, 65386531, 268540168, 1102884965, 4529509517, 18602535276, 76399953992, 313771907077, 1288650117266, 5292440423364, 21735865507300, 89268430356963, 366622284064081, 1505704745058057

Offset

0,3

Comments

r is the bronze ratio A098316.

Links

Table of n, a(n) for n=0..26.

Wikipedia, Metallic mean.

Index entries for linear recurrences with constant coefficients, signature (4,1,-2,-1,-1).

Formula

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

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

Mathematica

LinearRecurrence[{4, 1, -2, -1, -1}, {0, 1, 3, 12, 48}, 27] (* Amiram Eldar, May 02 2026 *)

Crossrefs

Cf. A080081, A098316, A395592.

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

Sequence in context: A113956 A323261 A103943 * A283679 A165328 A351282

Adjacent sequences: A395579 A395580 A395581 * A395583 A395584 A395585

Keyword

nonn,easy

Author

A.H.M. Smeets, Apr 29 2026

Status

approved