A033144 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.

1, 8, 64, 513, 4104, 32832, 262657, 2101256, 16810048, 134480385, 1075843080, 8606744640, 68853957121, 550831656968, 4406653255744, 35253226045953, 282025808367624, 2256206466940992, 18049651735527937, 144397213884223496, 1155177711073787968

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (8,0,1,-8).

Formula

a(n) = 8*a(n-1) + a(n-3) - 8*a(n-4).

G.f.: x / ((x-1)*(8*x-1)*(x^2+x+1)). - Colin Barker, Apr 30 2014

a(n) = round( (64/511)*8^n ). - Tani Akinari, Jul 15 2014

Mathematica

Module[{nn=30, d}, d=PadRight[{}, nn, {1, 0, 0}]; Table[FromDigits[Take[d, n], 8], {n, nn}]] (* or *) LinearRecurrence[{8, 0, 1, -8}, {1, 8, 64, 513}, 50] (* Harvey P. Dale, Nov 13 2013 *)
CoefficientList[Series[1/((x - 1) (8 x - 1) (x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, May 01 2014 *)

Prog

(PARI) Vec(x/((x-1)*(8*x-1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 30 2014

Crossrefs

Sequence in context: A074113 A074116 A245852 * A238300 A344271 A144317

Adjacent sequences: A033141 A033142 A033143 * A033145 A033146 A033147

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, Nov 13 2013

Status

approved