A021408 Decimal expansion of 1/404.

0, 0, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2, 4, 7, 5, 2

Offset

0,3

Comments

After the first two terms, a(n) is periodic with period 4: repeat [2, 4, 7, 5]. - Wesley Ivan Hurt, Jul 10 2016

Links

Table of n, a(n) for n=0..98.

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

Formula

From Wesley Ivan Hurt, Jul 10 2016: (Start)

G.f.: x^2*(2+2*x+5*x^2)/(1-x+x^2-x^3).

a(n) = a(n-1) - a(n-2) + a(n-3) for n>4, a(n) = a(n-4) for n>5.

a(n) = (9 + 5*cos(n*Pi/2) + sin(n*Pi/2))/2 for n>1. (End)

Example

0.0024752475247524752475247...

Maple

Digits:=100: evalf(1/404); # Wesley Ivan Hurt, Jul 10 2016

Mathematica

Join[{0, 0}, RealDigits[1/404, 10, 120][[1]]] (* or *) PadRight[{0, 0}, 120, {7, 5, 2, 4}] (* Harvey P. Dale, May 18 2012 *)
CoefficientList[Series[x^2*(2 + 2*x + 5*x^2)/(1 - x + x^2 - x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 10 2016 *)

Prog

(Magma) [0, 0] cat &cat [[2, 4, 7, 5]^^30]; // Wesley Ivan Hurt, Jul 10 2016

Crossrefs

Sequence in context: A167280 A236629 A019966 * A011178 A136790 A073158

Adjacent sequences: A021405 A021406 A021407 * A021409 A021410 A021411

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved