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*(x+1)/((x-1)*(4*x-1)*(1+x+x^2)). - Vincenzo Librandi, Jun 21 2012
a(n) = floor( (20/63)*4^n ). - Tani Akinari, Jul 16 2014
EXAMPLE
The first six terms have base-4 representations 1, 11, 110, 1101, 11011, 110110.
MATHEMATICA
LinearRecurrence[{4, 0, 1, -4}, {1, 4, 17, 69}, 30] (* Vincenzo Librandi, Jun 21 2012 *)
With[{nn=30}, Table[FromDigits[PadRight[{}, n, {1, 1, 0}], 4], {n, nn}]] (* Harvey P. Dale, Oct 22 2015 *)
PROG
(Magma) I:=[1, 5, 20, 81]; [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
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved