A033140 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.

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

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

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).

Programs

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

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 *)

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