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A033140
Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.
4
1, 4, 16, 65, 260, 1040, 4161, 16644, 66576, 266305, 1065220, 4260880, 17043521, 68174084, 272696336, 1090785345, 4363141380, 17452565520, 69810262081, 279241048324, 1116964193296, 4467856773185, 17871427092740, 71485708370960
OFFSET
1,2
FORMULA
a(n) = +4*a(n-1) +a(n-3) -4*a(n-4). G.f.: x / ( (x-1)*(4*x-1)*(1+x+x^2) ). - R. J. Mathar, Jan 08 2011
MATHEMATICA
LinearRecurrence[{4, 0, 1, -4}, {1, 4, 16, 65}, 30] (* Vincenzo Librandi, Jun 21 2012 *)
Table[FromDigits[PadRight[{}, n, {1, 0, 0}], 4], {n, 30}] (* Harvey P. Dale, Apr 15 2018 *)
PROG
(Magma) I:=[1, 4, 16, 65]; [n le 4 select I[n] else 4*Self(n-1)+Self(n-3)-4*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 21 2012
CROSSREFS
Sequence in context: A013149 A175065 A373280 * A181879 A243872 A052927
KEYWORD
nonn,base,easy
STATUS
approved