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

Author

Ant King, Jan 24 2012

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

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).

Crossrefs

Cf. A000217, A000290, A001108, A010879.

Programs

Magma

&cat[[1, 8, 9, 8, 1, 0]: n in [0..20]]; // Wesley Ivan Hurt, Jun 18 2016

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 *)

PARI

a(n)=[0, 1, 8, 9, 8, 1][n%6+1] \\ Charles R Greathouse IV, Jul 17 2016

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))).