The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A047300 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A047300

Numbers that are congruent to {2, 3, 4, 6} mod 7.
(history; published version)

#13 by Charles R Greathouse IV at Thu Sep 08 08:44:56 EDT 2022

PROG

(MAGMAMagma) [n : n in [0..150] | n mod 7 in [2, 3, 4, 6]]; // Wesley Ivan Hurt, Jun 02 2016

Discussion

Thu Sep 08

08:44

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

#12 by Joerg Arndt at Fri Jun 03 11:12:22 EDT 2016

STATUS

proposed

approved

#11 by Wesley Ivan Hurt at Fri Jun 03 10:52:02 EDT 2016

STATUS

editing

proposed

#10 by Wesley Ivan Hurt at Thu Jun 02 21:32:37 EDT 2016

DATA

2, 3, 4, 6, 9, 10, 11, 13, 16, 17, 18, 20, 23, 24, 25, 27, 30, 31, 32, 34, 37, 38, 39, 41, 44, 45, 46, 48, 51, 52, 53, 55, 58, 59, 60, 62, 65, 66, 67, 69, 72, 73, 74, 76, 79, 80, 81, 83, 86, 87, 88, 90, 93, 94, 95, 97, 100, 101, 102, 104, 107, 108, 109, 111

LINKS

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

FORMULA

G.f. : x*(2+x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar, _, Oct 25 2011

From Wesley Ivan Hurt, Jun 02 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14*n-5-i^(2*n)-(1-3*i)*i^(-n)-(1+3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047348(k). (End)

MAPLE

A047300:=n->(14*n-5-I^(2*n)-(1-3*I)*I^(-n)-(1+3*I)*I^n)/8: seq(A047300(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Table[(14n-5-I^(2n)-(1-3*I)*I^(-n)-(1+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [2, 3, 4, 6]]; // Wesley Ivan Hurt, Jun 02 2016

CROSSREFS

Cf. A047280, A047348.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#9 by Charles R Greathouse IV at Sat Jun 13 00:49:56 EDT 2015

LINKS

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

Discussion

Sat Jun 13

00:49

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

#8 by Charles R Greathouse IV at Fri Jun 12 15:24:43 EDT 2015

LINKS

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

Discussion

Fri Jun 12

15:24

OEIS Server: https://oeis.org/edit/global/2436

#7 by Russ Cox at Fri Mar 30 16:48:25 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

#6 by R. J. Mathar at Tue Oct 25 10:54:45 EDT 2011

STATUS

editing

approved

#5 by R. J. Mathar at Tue Oct 25 10:35:27 EDT 2011

LINKS

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

FORMULA

G.f. x*(2+x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).