The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A047429 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A047429

Numbers that are congruent to {4, 5, 6} mod 8.
(history; published version)

#19 by Charles R Greathouse IV at Thu Sep 08 08:44:57 EDT 2022

PROG

(MAGMAMagma) [n : n in [0..150] | n mod 8 in [4..6]]; // Wesley Ivan Hurt, Jun 09 2016

Discussion

Thu Sep 08

08:44

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

#18 by Michel Marcus at Fri Jun 10 10:07:15 EDT 2016

STATUS

reviewed

approved

#17 by Bruno Berselli at Fri Jun 10 08:48:30 EDT 2016

STATUS

proposed

reviewed

#16 by Wesley Ivan Hurt at Fri Jun 10 07:46:46 EDT 2016

STATUS

editing

proposed

#15 by Wesley Ivan Hurt at Thu Jun 09 11:32:19 EDT 2016

DATA

4, 5, 6, 12, 13, 14, 20, 21, 22, 28, 29, 30, 36, 37, 38, 44, 45, 46, 52, 53, 54, 60, 61, 62, 68, 69, 70, 76, 77, 78, 84, 85, 86, 92, 93, 94, 100, 101, 102, 108, 109, 110, 116, 117, 118, 124, 125, 126, 132, 133, 134, 140, 141, 142, 148, 149, 150, 156, 157

LINKS

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

FORMULA

G.f. : x*(4+x+x^2+2*x^3) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar, _, Dec 07 2011

a(n) = 5*A002264(n-1)+n+3 = A047475(n)+3. - _Bruno Berselli, _, Dec 07 2011

From Wesley Ivan Hurt, Jun 09 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (24*n-3-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-3, a(3k-2) = 8k-4. (End)

MAPLE

A047429:=n->(24*n-3-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047429(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [4..6]]; // Wesley Ivan Hurt, Jun 09 2016

CROSSREFS

Cf. A002264, A047475.

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#14 by Charles R Greathouse IV at Sat Jun 13 00:49:58 EDT 2015

LINKS

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

Discussion

Sat Jun 13

00:49

OEIS Server: https://oeis.org/edit/global/2439

#13 by Charles R Greathouse IV at Fri Jun 12 15:32:29 EDT 2015

LINKS

<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

Discussion

Fri Jun 12

15:32

OEIS Server: https://oeis.org/edit/global/2437

#12 by Charles R Greathouse IV at Thu Nov 21 13:09:01 EST 2013

MATHEMATICA

Select[Range[134], MemberQ[{4, 5, 6}, Mod[#, 8]]&] (* _Bruno Berselli, _, Dec 07 2011 *)

Discussion

Thu Nov 21

13:09

OEIS Server: https://oeis.org/edit/global/2064

#11 by Russ Cox at Fri Mar 30 16:48:26 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com)_.

Discussion

Fri Mar 30

16:48

OEIS Server: https://oeis.org/edit/global/110

#10 by R. J. Mathar at Wed Dec 07 07:58:11 EST 2011

STATUS

proposed

approved