A053794 a(n) = (n^2 + n) modulo 8.

0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0, 0, 2, 6, 4, 4, 6, 2, 0

Offset: 0

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), Mar 27 2000

Keywords

• nonn
• easy

Comments

Periodic with period 8.

Links

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

Crossrefs

Cf. A053793, A105198.

Programs

Mathematica

PadRight[{}, 105, {0, 2, 6, 4, 4, 6, 2, 0}] (* Michael De Vlieger, Jun 22 2022 *)

PARI

A053794(n)=[0, 2, 6, 4, 4, 6, 2, 0][n%8+1] \\ M. F. Hasler, Aug 27 2012

Scheme

(define (A053794 n) (modulo (+ (* n n) n) 8)) ;; Antti Karttunen, Aug 10 2017

Formula

From Wesley Ivan Hurt, Jun 22 2022: (Start)

a(n) = 2*A105198(n).

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

Extensions

More terms from James Sellers, Apr 08 2000

Extended to n=103 by Antti Karttunen, Aug 10 2017