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

Author

Vincenzo Librandi, Sep 24 2009

Keywords

• nonn
• easy
• less

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

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

Crossrefs

Cf. A008865, A053796, A147973.

Programs

Magma

[(2*n^2+8*n+4) mod 10 : n in [0..100]]; // Wesley Ivan Hurt, Sep 06 2014

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 *)

PARI

a(n)=[4,4,8,6,8][n%5+1] \\ Edward Jiang, Sep 06 2014

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)

Extensions

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

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