A033122 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 4, 17, 69, 276, 1105, 4421, 17684, 70737, 282949, 1131796, 4527185, 18108741, 72434964, 289739857, 1158959429, 4635837716, 18543350865, 74173403461, 296693613844, 1186774455377, 4747097821509, 18988391286036, 75953565144145

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Formula

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

G.f.: x*(1+x^2)/((1-x)*(1-4*x)*(1+x+x^2)). [Bruno Berselli, Jun 20 2012]

Mathematica

LinearRecurrence[{4, 0, 1, -4}, {1, 4, 17, 69}, 30] (* Vincenzo Librandi, Jun 20 2012 *)
Table[FromDigits[PadRight[{}, n, {1, 0, 1}], 4], {n, 30}] (* Harvey P. Dale, Jul 17 2018 *)

Prog

(Magma) I:=[1, 4, 17, 69]; [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 20 2012

Crossrefs

Sequence in context: A096881 A363588 A344217 * A330246 A339065 A005511

Adjacent sequences: A033119 A033120 A033121 * A033123 A033124 A033125

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved