A033142 Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.

1, 6, 36, 217, 1302, 7812, 46873, 281238, 1687428, 10124569, 60747414, 364484484, 2186906905, 13121441430, 78728648580, 472371891481, 2834231348886, 17005388093316, 102032328559897, 612193971359382, 3673163828156292, 22038982968937753, 132233897813626518

Offset

1,2

Links

Table of n, a(n) for n=1..23.

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

Formula

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

G.f.: x/((1-x^3)*(1-6*x)) = 36/(215*(1-6*x))+(-6*x^2-x-36)/(215*(1-x^3)). - Tani Akinari, Jul 18 2014

a(n) = floor((36/215)*6^n). - Tani Akinari, Jul 18 2014

Mathematica

LinearRecurrence[{6, 0, 1, -6}, {1, 6, 36, 217}, 30] (* or *)
Floor[36/215*6^Range[30]] (* Paolo Xausa, Feb 02 2024 *)

Prog

(PARI) Vec(x/((1-x^3)*(1-6*x)) + O(x^50)) \\ Tani Akinari, Jul 18 2014

Crossrefs

Sequence in context: A050736 A196869 A172489 * A082309 A004319 A129324

Adjacent sequences: A033139 A033140 A033141 * A033143 A033144 A033145

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved