A037521 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 2, 1, 0.

2, 9, 36, 146, 585, 2340, 9362, 37449, 149796, 599186, 2396745, 9586980, 38347922, 153391689, 613566756, 2454267026, 9817068105, 39268272420, 157073089682, 628292358729, 2513169434916, 10052677739666, 40210710958665

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

a(n) = floor(4^(n+1)/7). - Mircea Merca, Dec 26 2010

G.f.: x*(2+x) / ( (1-x)*(1-4*x)*(1+x+x^2) ).

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

a(n) = 4^(n+1)/7 - 1/3 - (-1)^(n mod 3)*A167380(4 + (n mod 3))/21 = 2*A033140(n) + A033140(n-1). - R. J. Mathar, Jan 08 2011

Maple

seq(floor(4^(n+1)/7), n=1..30); # Mircea Merca, Dec 26 2010

Mathematica

Table[FromDigits[PadRight[{}, n, {2, 1, 0}], 4], {n, 30}] (* Harvey P. Dale, Jul 03 2017 *)

Prog

(Magma) [Floor(4^(n+1)/7) : n in [1..30]]; // Vincenzo Librandi, Jun 25 2011

Crossrefs

Sequence in context: A077836 A003125 A055841 * A037730 A029874 A052834

Adjacent sequences: A037518 A037519 A037520 * A037522 A037523 A037524

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved