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Revision History for A080457

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A080457

a(1)=3; for n>1, a(n)=a(n-1) if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
(history; published version)

#11 by Michel Marcus at Wed Jul 15 16:35:24 EDT 2015

STATUS

editing

proposed

#10 by Michel Marcus at Wed Jul 15 16:35:18 EDT 2015

LINKS

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/indexVOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

STATUS

proposed

editing

#9 by Wesley Ivan Hurt at Wed Jul 15 15:10:39 EDT 2015

STATUS

editing

proposed

#8 by Wesley Ivan Hurt at Wed Jul 15 15:09:32 EDT 2015

LINKS

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

FORMULA

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

MAPLE

A080457:=n->3+4*(n-2-floor((n-3)/4)): seq(A080457(n), n=1..100); # Wesley Ivan Hurt, Jul 15 2015

MATHEMATICA

CoefficientList[Series[(3 + 4 x + 4 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Jul 15 2015 *)

PROG

(MAGMA) [3+4*(n-2-Floor((n-3)/4)) : n in [1..100]]; // Wesley Ivan Hurt, Jul 15 2015

AUTHOR

N. J. A. Sloane and _Benoit Cloitre, _, Mar 20 2003

#7 by Wesley Ivan Hurt at Wed Jul 15 12:43:50 EDT 2015

FORMULA

From Wesley Ivan Hurt, Jul 15 2015: (Start)

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

a(n) = (6*n-1+(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/2. (End)

CROSSREFS

Cf. A080455-A080458, A080036, A080037, A080455, A080456, A080457, A080458.

KEYWORD

nonn,easy

STATUS

approved

editing

#6 by Russ Cox at Fri Mar 30 16:49:38 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com) _ and Benoit Cloitre, Mar 20 2003

Discussion

Fri Mar 30

16:49

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

#5 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) and Benoit Cloitre, Mar 20 2003

#4 by N. J. A. Sloane at Sat Apr 09 03:00:00 EDT 2005

LINKS

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

LINKS

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.mathcs.uwaterloo.ca/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

LINKS

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.researchmath.attuwaterloo.com/~njasca/docJIS/aronindex.txthtml">Numerical analogues of Aronson's sequence</a> , J. Integer Seqs., Vol. 6 (submitted2003), #03.2.2.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308)

KEYWORD

nonn,new

nonn