A080458 - OEIS

%I #26 Feb 13 2020 06:47:24

%S 4,8,12,12,16,20,24,24,28,32,36,36,40,44,48,48,52,56,60,60,64,68,72,

%T 72,76,80,84,84,88,92,96,96,100,104,108,108,112,116,120,120,124,128,

%U 132,132,136,140,144,144,148,152,156,156,160,164,168,168,172,176

%N a(1)=4; 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="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.

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

%F a(n) = 4 + 4*(n-2-floor((n-4)/4)).

%F From _Chai Wah Wu_, Jul 17 2016: (Start)

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

%F G.f.: 4*x*(x^2 + x + 1)/(x^5 - x^4 - x + 1). (End)

%F From _Ilya Gutkovskiy_, Jul 17 2016: (Start)

%F E.g.f.: (3*x + 1)*cosh(x) + (3*x + 2)*sinh(x) - cos(x) - sin(x).

%F a(n) = (6*n - (-1)^n - 2*sqrt(2)*sin(Pi*n/2+Pi/4) + 3)/2. (End)

%t LinearRecurrence[{1, 0, 0, 1, -1}, {4, 8, 12, 12, 16}, 60] (* _Jean-François Alcover_, Sep 20 2018 *)

%o (PARI) a(n) = 4 + 4*(n-2-(n-4)\4); \\ _Michel Marcus_, May 06 2016

%Y Cf. A080455, A080456, A080457, A080036, A080037.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_ and _Benoit Cloitre_, Mar 20 2003