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A080455 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. 13
1, 5, 9, 13, 13, 17, 21, 25, 25, 29, 33, 37, 37, 41, 45, 49, 49, 53, 57, 61, 61, 65, 69, 73, 73, 77, 81, 85, 85, 89, 93, 97, 97, 101, 105, 109, 109, 113, 117, 121, 121, 125, 129, 133, 133, 137, 141, 145, 145, 149, 153, 157, 157, 161, 165, 169, 169, 173 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

For m>=1, a(4m) = a(4m+1) = 12m+1, a(4m+2) = 12m+5, a(4m+3) = 12m+9.

Or, shorter: a(n) = 4*n+1- 4*floor((n+3)/4). - Benoit Cloitre, Mar 20 2003

From Colin Barker, Oct 16 2013: (Start)

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

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

MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 5, 9, 13, 13}, 58] (* Jean-Fran├žois Alcover, Sep 21 2017 *)

PROG

(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

CROSSREFS

Cf. A080456-A080458, A080036, A080037.

Sequence in context: A079355 A080781 A079357 * A122798 A241987 A189464

Adjacent sequences:  A080452 A080453 A080454 * A080456 A080457 A080458

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 20 2003

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)