A037513 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,1.

2, 8, 33, 134, 536, 2145, 8582, 34328, 137313, 549254, 2197016, 8788065, 35152262, 140609048, 562436193, 2249744774, 8998979096, 35995916385, 143983665542, 575934662168, 2303738648673, 9214954594694, 36859818378776

Offset

1,1

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

G.f.: x*(2+x^2) / ( (x-1)*(4*x-1)*(1 + x + x^2) ). - R. J. Mathar, Nov 21 2011

a(n) = 4*a(n-1) + a(n-3) - 4*a(n-4). - Vincenzo Librandi, Jun 22 2012

Mathematica

LinearRecurrence[{4, 0, 1, -4}, {2, 8, 33, 134}, 40] (* Vincenzo Librandi, Jun 22 2012 *)
Module[{nn=30, c}, c=PadRight[{}, nn, {2, 0, 1}]; Table[FromDigits[Take[c, n], 4], {n, nn}]] (* Harvey P. Dale, May 28 2014 *)

Prog

(Magma) I:=[2, 8, 33, 134]; [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 22 2012
(PARI) x='x+O('x^99); Vec(x*(2+x^2)/((x-1)*(4*x-1)*(1+x+x^2))) \\ Altug Alkan, Sep 21 2018

Crossrefs

Sequence in context: A135620 A134708 A294530 * A037716 A373752 A279014

Adjacent sequences: A037510 A037511 A037512 * A037514 A037515 A037516

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved