A037583 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 3,1.

3, 13, 55, 221, 887, 3549, 14199, 56797, 227191, 908765, 3635063, 14540253, 58161015, 232644061, 930576247, 3722304989, 14889219959, 59556879837, 238227519351, 952910077405, 3811640309623, 15246561238493, 60986244953975

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(3+x) / ( (x-1)*(4*x-1)*(1+x) ). - R. J. Mathar, Apr 26 2015

a(n) = floor(13*4^n/15). - Karl V. Keller, Jr., Aug 04 2021

Example

In base 4, we get: 3, 31, 313, 3131, 31313, 313131, 3131313, 31313131, ... = A037589.

Mathematica

Table[FromDigits[PadRight[{}, n, {3, 1}], 4], {n, 30}] (* or *) LinearRecurrence[ {4, 1, -4}, {3, 13, 55}, 30] (* Harvey P. Dale, Sep 20 2020 *)

Prog

(Python) print([13*4**n//15 for n in range(1, 30)]) # Karl V. Keller, Jr., Aug 04 2021

Crossrefs

Cf. A007090, A037584, A037585, A037586, A037587, A037588, A037589.

Sequence in context: A308349 A367153 A140320 * A302757 A093834 A372414

Adjacent sequences: A037580 A037581 A037582 * A037584 A037585 A037586

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved