A165662 Period 5: repeat 4,4,8,6,8.

4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8

Offset

0,1

Comments

This is also the post-period decimal digit of ((n+2)^2-2)/5.

Serves also as the decimal expansion of 1495600/33333 and as the continued fraction representation of (33397+sqrt(12952802))/1649.

Links

Table of n, a(n) for n=0..89.

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

Formula

a(n) = (2*n^2 + 8*n + 4) mod 10.

From Wesley Ivan Hurt, Sep 06 2014: (Start)

G.f.: 2*(2 + 2*x + 4*x^2 + 3*x^3 + 4*x^4)/(1-x^5). [corrected by Georg Fischer, May 11 2019]

Recurrence: a(n) = a(n-5).

a(n) = (2*A008865(n+1)) mod 10.

a(n) = (-A147973(n+4)) mod 10.

a(n+1) = 2*A053796(n) + 4. (End)

Maple

A165662:=n->2*n^2+8*n+4 mod 10: seq(A165662(n), n=0..100); # Wesley Ivan Hurt, Sep 06 2014

Mathematica

Table[Mod[2 n^2 + 8 n + 4, 10], {n, 0, 100}] (* Wesley Ivan Hurt, Sep 06 2014 *)
CoefficientList[Series[2 (2 + 2 x + 4 x^2 + 3 x^3 + 4 x^4)/(1 - x^5), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 06 2014 *)

Prog

(Magma) [(2*n^2+8*n+4) mod 10 : n in [0..100]]; // Wesley Ivan Hurt, Sep 06 2014
(PARI) a(n)=[4, 4, 8, 6, 8][n%5+1] \\ Edward Jiang, Sep 06 2014

Crossrefs

Cf. A008865, A053796, A147973.

Sequence in context: A254267 A028266 A275982 * A110648 A198936 A289091

Adjacent sequences: A165659 A165660 A165661 * A165663 A165664 A165665

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Sep 24 2009

Extensions

Definition simplified, offset corrected by R. J. Mathar, Sep 25 2009

Name and offset changed by Wesley Ivan Hurt, Sep 06 2014

Status

approved