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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.
0
1, 6, 36, 217, 1302, 7812, 46873, 281238, 1687428, 10124569, 60747414, 364484484, 2186906905, 13121441430, 78728648580, 472371891481, 2834231348886, 17005388093316, 102032328559897, 612193971359382, 3673163828156292, 22038982968937753, 132233897813626518
OFFSET
1,2
FORMULA
a(n) = 6a(n-1) + a(n-3) - 6a(n-4).
G.f.: x/((1-x^3)*(1-6*x)) = 36/(215*(1-6*x))+(-6*x^2-x-36)/(215*(1-x^3)). - Tani Akinari, Jul 18 2014
a(n) = floor((36/215)*6^n). - Tani Akinari, Jul 18 2014
MATHEMATICA
LinearRecurrence[{6, 0, 1, -6}, {1, 6, 36, 217}, 30] (* or *)
Floor[36/215*6^Range[30]] (* Paolo Xausa, Feb 02 2024 *)
PROG
(PARI) Vec(x/((1-x^3)*(1-6*x)) + O(x^50)) \\ Tani Akinari, Jul 18 2014
CROSSREFS
Sequence in context: A377115 A196869 A172489 * A082309 A004319 A129324
KEYWORD
nonn,base,easy
STATUS
approved