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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

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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).

From Tani Akinari, Jul 18 2014: (Start)

G.f.: x/((1-x^3)*(1-6*x)) = 36/(215*(1-6*x))+(-6*x^2-x-36)/(215*(1-x^3)).

a(n) = floor((36/215)*6^n). (End)

E.g.f.: (108*exp(6*x) - 43*exp(x) - 5*exp(-x/2)*(13*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)))/645. - Stefano Spezia, Sep 07 2025