A110550 Periodic {1,3,2,4,4,2,3,1}.

1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1, 1, 3, 2, 4, 4, 2, 3, 1

Offset: 0

Author

Paul Barry, Jul 26 2005

Keywords

• easy
• nonn

Comments

Permutation of {1,2,3,4} followed by its reversal, repeated.

Simple continued fraction expansion of (671 + sqrt 7241477)/2606. - R. J. Mathar, Mar 08 2012

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

Crossrefs

Cf. A105198, A110549.

Programs

Mathematica

PadRight[{}, 100, {1,3,2,4,4,2,3,1}] (* G. C. Greubel, Aug 31 2017 *)

PARI

x='x+O('x^50); Vec((x^2+3*x+1)*(x^2-x+1)/((1-x)*(1+x^4))) \\ G. C. Greubel, Aug 31 2017

Scheme

(define (A110550 n) (list-ref '(1 3 2 4 4 2 3 1) (modulo n 8))) ;; Antti Karttunen, Aug 10 2017

Formula

G.f.: -(x^2+3*x+1)*(x^2-x+1) / ( (x-1)*(1+x^4) ).

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7).