The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A176895 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A176895

Period 4: repeat [1, 4, 2, 4].
(history; published version)

#34 by Joerg Arndt at Tue Dec 12 07:40:22 EST 2023

STATUS

proposed

approved

#33 by Paolo P. Lava at Tue Dec 12 07:25:30 EST 2023

STATUS

editing

proposed

#32 by Paolo P. Lava at Tue Dec 12 07:25:26 EST 2023

FORMULA

a(n) = (1/24)*{29*(n mod 4)-[(n+1) mod 4]+23*[(n+2) mod 4]-7*[(n+3) mod 4]}. - Paolo P. Lava, Apr 30 2010

a(n) = (11-I^n-5*(-1)^n-(-I)^n)/4 = 11/4-5*(-1)^n/4 -A056594(n)/2, with I=sqrt(-1). - Paolo P. Lava, Apr 30 2010

STATUS

approved

editing

#31 by Charles R Greathouse IV at Thu Sep 08 08:45:53 EDT 2022

PROG

(MAGMAMagma) &cat [[1, 4, 2, 4]^^30]; // Wesley Ivan Hurt, Jul 11 2016

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#30 by Bruno Berselli at Wed Jul 13 04:20:47 EDT 2016

STATUS

reviewed

approved

#29 by Michel Marcus at Mon Jul 11 11:16:42 EDT 2016

STATUS

proposed

reviewed

#28 by Wesley Ivan Hurt at Mon Jul 11 11:12:46 EDT 2016

STATUS

editing

proposed

#27 by Wesley Ivan Hurt at Mon Jul 11 11:12:37 EDT 2016

NAME

Period 4: repeat [1, 4, 2, 4].

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

FORMULA

a(n) = (1/24)*{29*(n mod 4)-[(n+1) mod 4]+23*[(n+2) mod 4]-7*[(n+3) mod 4]}. - Paolo P. Lava, Apr 30 2010

a(n) = (11-I^n-5*(-1)^n-(-I)^n)/4 = 11/4-5*(-1)^n/4 -A056594(n)/2, with I=sqrt(-1). - Paolo P. Lava, Apr 30 2010

G.f. : ( -1-+4*x-+2*x^2-+4*x^3 ) / ( (x-1-x)*(1+x)*(x^2+1) ). - R. J. Mathar, Mar 21 2011

From Wesley Ivan Hurt, Jul 11 2016: (Start)

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

a(n) = 2^((5-(-I)^n-I^n-3*I^(2*n))/4) where I=sqrt(-1). (End)

MAPLE

seq(op([1, 4, 2, 4]), n=0..50); # Wesley Ivan Hurt, Jul 11 2016

MATHEMATICA

PadRight[{}, 100, {1, 4, 2, 4}] (* Wesley Ivan Hurt, Jul 11 2016 *)

PROG

(MAGMA) &cat [[1, 4, 2, 4]^^30]; // Wesley Ivan Hurt, Jul 11 2016

CROSSREFS

Cf. A056594.

STATUS

approved

editing

#26 by Charles R Greathouse IV at Wed Oct 07 10:42:58 EDT 2015

STATUS

editing

approved

#25 by Charles R Greathouse IV at Wed Oct 07 10:42:54 EDT 2015

PROG

(PARI) a(n)=4/gcd(n, 4) \\ Charles R Greathouse IV, Oct 07 2015

STATUS

approved

editing