A037597 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0.

1, 7, 28, 113, 455, 1820, 7281, 29127, 116508, 466033, 1864135, 7456540, 29826161, 119304647, 477218588, 1908874353, 7635497415, 30541989660, 122167958641, 488671834567, 1954687338268, 7818749353073, 31274997412295

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Formula

a(n) = floor(4^(n+1)/9). - Mircea Merca, Dec 26 2010

From Joerg Arndt, Jan 08 2011: (Start)

G.f.: x*(1+3*x) / ( (x-1)*(4*x-1)*(1+x+x^2) ).

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

a(1)=1, a(2)=7, a(n) = 5*a(n-1) - 4*a(n-2) + (period 3: repeat -3, 1, 2). - Vincenzo Librandi, Jun 06 2011

E.g.f.: 2*(2*exp(x)*(exp(3*x) - 1) - sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/x))/9. - Stefano Spezia, Oct 02 2023

Maple

seq(floor(4^(n+1)/9), n=1..32); # Mircea Merca, Dec 28 2010

Prog

(Magma) [Floor(4^(n+1)/9): n in [1..30]]; // Vincenzo Librandi, May 22 2011
(PARI) a(n)=4^(n+1)\9 \\ Charles R Greathouse IV, Jun 06 2011

Crossrefs

Cf. A178744.

Sequence in context: A002042 A200666 A207098 * A037702 A359018 A302523

Adjacent sequences: A037594 A037595 A037596 * A037598 A037599 A037600

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved