|
%I #19 Sep 21 2017 11:58:21
%S 1,5,9,13,13,17,21,25,25,29,33,37,37,41,45,49,49,53,57,61,61,65,69,73,
%T 73,77,81,85,85,89,93,97,97,101,105,109,109,113,117,121,121,125,129,
%U 133,133,137,141,145,145,149,153,157,157,161,165,169,169,173
%N a(1)=1; for n>1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.
%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H 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)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F For m>=1, a(4m) = a(4m+1) = 12m+1, a(4m+2) = 12m+5, a(4m+3) = 12m+9.
%F Or, shorter: a(n) = 4*n+1- 4*floor((n+3)/4). - _Benoit Cloitre_, Mar 20 2003
%F From _Colin Barker_, Oct 16 2013: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5).
%F G.f.: -x*(x^4 - 4*x^3 - 4*x^2 - 4*x - 1) / ((x-1)^2*(x+1)*(x^2+1)). (End)
%t LinearRecurrence[{1, 0, 0, 1, -1}, {1, 5, 9, 13, 13}, 58] (* _Jean-François Alcover_, Sep 21 2017 *)
%o (PARI) Vec(-x*(x^4-4*x^3-4*x^2-4*x-1)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ _Colin Barker_, Oct 16 2013
%Y Cf. A080456-A080458, A080036, A080037.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Mar 20 2003
|
