A033133 Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0.

1, 7, 42, 253, 1519, 9114, 54685, 328111, 1968666, 11811997, 70871983, 425231898, 2551391389, 15308348335, 91850090010, 551100540061, 3306603240367, 19839619442202, 119037716653213, 714226299919279, 4285357799515674, 25712146797094045, 154272880782564271

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,0,1,-6).

Formula

a(n) = 6*a(n-1) + a(n-3) - 6*a(n-4).

G.f.: x*(1+x) / ((1-x)*(1-6*x)*(1+x+x^2)). - Colin Barker, Dec 24 2015

a(n) = floor(42*6^n/215). - Christian Krause, May 19 2026

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 1, 0}], 6], {n, 30}] (* Harvey P. Dale, Apr 15 2026 *)
(* Alternative: *)
LinearRecurrence[{6, 0, 1, -6}, {1, 7, 42, 253}, 30] (* Harvey P. Dale, Apr 15 2026 *)

Prog

(PARI) Vec(x*(1+x)/((1-x)*(1-6*x)*(1+x+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015

Crossrefs

Sequence in context: A170688 A003949 A252700 * A385823 A082035 A127016

Adjacent sequences: A033130 A033131 A033132 * A033134 A033135 A033136

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Status

approved