A205185 Period 6: repeat [1, 8, 9, 8, 1, 0].

1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8, 9, 8, 1, 0, 1, 8

Offset

1,2

Comments

The terms of this sequence are the units' digits of the indices of those nonzero triangular numbers that are also perfect squares (A001108).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(1+7x+x^2) / ((1-x)*(1+x)*(1-x+x^2)).

a(n) = a(n-6) for n>6.

a(n) = 9-a(n-3) for n>3.

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

a(n) = 1/6*(27+(-1)^n*(5-32*cos(2*n*Pi/3))).

Example

As the fourth nonzero triangular number that is also a perfect square is A000217(288), and 288 has units' digit A010879(288)=8, then a(4)=8.

Maple

A205185:=n->[1, 8, 9, 8, 1, 0][(n mod 6)+1]: seq(A205185(n), n=0..100); # Wesley Ivan Hurt, Jun 18 2016

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 8, 9, 8, 1, 0}, 86]
PadRight[{}, 100, {1, 8, 9, 8, 1, 0}] (* Vincenzo Librandi, Jun 19 2016 *)

Prog

(Magma) &cat[[1, 8, 9, 8, 1, 0]: n in [0..20]]; // Wesley Ivan Hurt, Jun 18 2016
(PARI) a(n)=[0, 1, 8, 9, 8, 1][n%6+1] \\ Charles R Greathouse IV, Jul 17 2016

Crossrefs

Cf. A000217, A000290, A001108, A010879.

Sequence in context: A154582 A020507 A195341 * A011463 A073637 A153202

Adjacent sequences: A205182 A205183 A205184 * A205186 A205187 A205188

Keyword

nonn,easy

Author

Ant King, Jan 24 2012

Status

approved