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A080460 a(1) = 2; for n > 1, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 4 otherwise. 0

%I

%S 2,2,6,10,14,14,18,22,26,26,30,34,38,38,42,46,50,50,54,58,62,62,66,70,

%T 74,74,78,82,86,86,90,94,98,98,102,106,110,110,114,118,122,122,126,

%U 130,134,134,138,142,146,146,150,154,158,158,162,166,170,170

%N a(1) = 2; 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>, 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) = 2 + 4*(n - 2 - floor((n - 2)/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.: 2*x*(x^4 + 2*x^3 + 2*x^2 + 1)/(x^5 - x^4 - x + 1). (End)

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

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

%F a(n) = (6*n - (-1)^n + 2*sqrt(2)*sin(Pi*n/2 + Pi/4) - 5)/2. (End)

%t LinearRecurrence[{1, 0, 0, 1, -1}, {2, 2, 6, 10, 14}, 58] (* _Jean-Fran├žois Alcover_, Jan 07 2019 *)

%o (PARI) a(n)=4*n - (n-2)\4*4 - 6 \\ _Charles R Greathouse IV_, Jul 17 2016

%Y Cf. A080455, A080456, A080457, A080458, A080036, A080037.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_ and Benoit Cloitre, Mar 22 2003

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Last modified May 30 18:07 EDT 2020. Contains 334728 sequences. (Running on oeis4.)