A037608 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,3.

1, 10, 83, 665, 5322, 42579, 340633, 2725066, 21800531, 174404249, 1395233994, 11161871955, 89294975641, 714359805130, 5714878441043, 45719027528345, 365752220226762, 2926017761814099, 23408142094512793, 187265136756102346, 1498121094048818771

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,0,1,-8).

Formula

a(n) = 8*a(n-1)+a(n-3)-8*a(n-4). - Colin Barker, Nov 28 2014

G.f.: x*(3*x^2+2*x+1) / ((x-1)*(8*x-1)*(x^2+x+1)). - Colin Barker, Nov 28 2014

Example

1, 10, 83, 665, 5322, ... in base 8 are 1, 12, 123, 1231, 12312, ...

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 2, 3}], 8], {n, 30}] (* Harvey P. Dale, Apr 06 2022 *)

Prog

(PARI) Vec(x*(3*x^2+2*x+1)/((x-1)*(8*x-1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Nov 28 2014

Crossrefs

Cf. A037610.

Sequence in context: A116879 A154340 A037699 * A055149 A014831 A048440

Adjacent sequences: A037605 A037606 A037607 * A037609 A037610 A037611

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved