A033124 Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 6, 37, 223, 1338, 8029, 48175, 289050, 1734301, 10405807, 62434842, 374609053, 2247654319, 13485925914, 80915555485, 485493332911, 2912959997466, 17477759984797, 104866559908783, 629199359452698, 3775196156716189, 22651176940297135, 135907061641782810

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

a(n) = round( (37/215)*6^n ). - Tani Akinari, Jul 15 2014

G.f.: x*(x^2+1) / ((x-1)*(6*x-1)*(x^2+x+1)). - Colin Barker, Jul 15 2014

Example

The first six terms have base 6 representations 1, 10, 101, 1011, 10110, 101101. - Michel Marcus, Jul 17 2014

Maple

A033124 := proc(n)
    coeftayl( (x*(x^2+1) / ((x-1)*(6*x-1)*(x^2+x+1)), x=0, n));
end proc:
seq(A033124(n), n=1..30); # Wesley Ivan Hurt, Jul 17 2014

Mathematica

CoefficientList[Series[(x^2 + 1)/((x - 1)*(6*x - 1)*(x^2 + x + 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 17 2014 *)

Prog

(PARI) Vec(x*(x^2+1)/((x-1)*(6*x-1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Jul 15 2014
(Magma) [Round((37/215)*6^n) : n in [1..30]]; // Wesley Ivan Hurt, Jul 17 2014

Crossrefs

Cf. A033128 (similar in base 10).

Sequence in context: A081152 A244618 A033116 * A288786 A180032 A022035

Adjacent sequences: A033121 A033122 A033123 * A033125 A033126 A033127

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Colin Barker, Jul 15 2014

Status

approved