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

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

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

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