A033126 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 8, 65, 521, 4168, 33345, 266761, 2134088, 17072705, 136581641, 1092653128, 8741225025, 69929800201, 559438401608, 4475507212865, 35804057702921, 286432461623368, 2291459692986945, 18331677543895561, 146653420351164488, 1173227362809315905, 9385818902474527241

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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).

a(n) = floor( (65/511)*8^n ). - Tani Akinari, Jul 15 2014

G.f.: x*(x^2+1) / ((x-1)*(8*x-1)*(x^2+x+1)). - Colin Barker, Jul 17 2014

Example

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

Maple

A033126 := proc(n)
    coeftayl( x*(x^2+1) / ((x-1)*(8*x-1)*(x^2+x+1)), x=0, n) ;
end proc:
seq(A033126(n), n=1..30); # Wesley Ivan Hurt, Jul 17 2014

Mathematica

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

Prog

(PARI) a(n)=(65*8^n)\511; \\ Michel Marcus, Jul 16 2014
(Magma) [Floor( (65/511)*8^n ) : n in [1..30]]; // Wesley Ivan Hurt, Jul 17 2014

Crossrefs

Cf. A033128 (similar in base 10).

Sequence in context: A317600 A288788 A033118 * A022039 A041025 A163459

Adjacent sequences: A033123 A033124 A033125 * A033127 A033128 A033129

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Michel Marcus, Jul 16 2014

Status

approved