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A033131 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0. 1
1, 5, 20, 81, 325, 1300, 5201, 20805, 83220, 332881, 1331525, 5326100, 21304401, 85217605, 340870420, 1363481681, 5453926725, 21815706900, 87262827601, 349051310405, 1396205241620, 5584820966481, 22339283865925, 89357135463700 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Cf. A033137 (similar in base 10).
Sequence in context: A363508 A252698 A271196 * A321703 A022021 A165203
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified June 21 10:24 EDT 2024. Contains 373543 sequences. (Running on oeis4.)