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A037583 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 3,1. 1
3, 13, 55, 221, 887, 3549, 14199, 56797, 227191, 908765, 3635063, 14540253, 58161015, 232644061, 930576247, 3722304989, 14889219959, 59556879837, 238227519351, 952910077405, 3811640309623, 15246561238493, 60986244953975 (list; graph; refs; listen; history; text; internal format)
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: A305655 A308349 A140320 * A302757 A093834 A296045

Adjacent sequences:  A037580 A037581 A037582 * A037584 A037585 A037586

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 18 08:58 EDT 2021. Contains 348067 sequences. (Running on oeis4.)