A033126 - OEIS

%I #31 Sep 08 2022 08:44:51

%S 1,8,65,521,4168,33345,266761,2134088,17072705,136581641,1092653128,

%T 8741225025,69929800201,559438401608,4475507212865,35804057702921,

%U 286432461623368,2291459692986945,18331677543895561,146653420351164488,1173227362809315905,9385818902474527241

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

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (8,0,1,-8).

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

%F a(n) = floor( (65/511)*8^n ). - _Tani Akinari_, Jul 15 2014

%F G.f.: x*(x^2+1) / ((x-1)*(8*x-1)*(x^2+x+1)). - _Colin Barker_, Jul 17 2014

%e The first six terms have base 8 representations 1, 10, 101, 1011, 10110, 101101.

%p A033126 := proc(n)

%p     coeftayl( x*(x^2+1) / ((x-1)*(8*x-1)*(x^2+x+1)), x=0, n) ;

%p end proc:

%p seq(A033126(n), n=1..30); # _Wesley Ivan Hurt_, Jul 17 2014

%t CoefficientList[Series[(x^2 + 1)/((x - 1)*(8*x - 1)*(x^2 + x + 1)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jul 17 2014 *)

%t Table[FromDigits[PadRight[{},n,{1,0,1}],8],{n,30}] (* or *) LinearRecurrence[ {8,0,1,-8},{1,8,65,521},30] (* _Harvey P. Dale_, Sep 14 2016 *)

%o (PARI) a(n)=(65*8^n)\511; \\ _Michel Marcus_, Jul 16 2014

%o (Magma) [Floor( (65/511)*8^n ) : n in [1..30]]; // _Wesley Ivan Hurt_, Jul 17 2014

%Y Cf. A033128 (similar in base 10).

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_

%E More terms from _Michel Marcus_, Jul 16 2014