A199264 Period 18: repeat (9,8,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8).

9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5

Offset: 0

Author

Arkadiusz Wesolowski, Nov 04 2011

Keywords

• easy
• nonn

Comments

'Valley and Peak' sequence.

The sequence contains only values less than 10.

abs(a(n)-a(n+1)) = 1.

This sequence is in A158289. - Omar E. Pol, Feb 02 2012

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A158289.

Programs

Mathematica

Flatten[Table[{9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8}, {5}]] (* Arkadiusz Wesolowski, Dec 03 2011 *)
(* For Mathematica 7.0+ *) ArrayPad[Range[0, 9], {9, 68}, "Reflected"] (* Arkadiusz Wesolowski, Feb 02 2011 *)
Table[Abs[Mod[n, 18] - 9], {n, 0, 81}] (* Alonso del Arte, Jul 03 2012 *)
PadRight[{},90,Join[Range[9,0,-1],Range[8]]] (* Harvey P. Dale, Apr 08 2013 *)

PARI

a(n)=[9,8,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8][n%18+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = 9 - A158289(n).

G.f.: ( -9+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8-8*x^9 ) / ( (x-1)*(1+x)*(x^2-x+1)*(x^6-x^3+1) ). - R. J. Mathar, Nov 05 2011

a(n) = A158289(n+9). - Omar E. Pol, Feb 02 2012

a(n) = abs((n mod 18) - 9). - Alonso del Arte, Jul 03 2012