A061891 - OEIS

A061891

a(0) = 1; for n>0, a(n) = a(n-1) if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.

1, 1, 4, 7, 7, 10, 13, 13, 16, 19, 19, 22, 25, 25, 28, 31, 31, 34, 37, 37, 40, 43, 43, 46, 49, 49, 52, 55, 55, 58, 61, 61, 64, 67, 67, 70, 73, 73, 76, 79, 79, 82, 85, 85, 88, 91, 91, 94, 97, 97, 100, 103, 103, 106, 109, 109, 112, 115, 115, 118, 121, 121, 124

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..62.

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, arXiv:math/0305308 [math.NT], 2003.

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

FORMULA

a(n) = 2*n-1 if n == 1 (mod 3), 2*n if n == 2 (mod 3), 2*n + 1 if n == 0 (mod 3).

Differences are periodic with period 3.

From Colin Barker, Jun 20 2013: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4).

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

a(n) = 2*n + 1 - A080425(n) = 2*n - 1 + A010872(n+1). [Wesley Ivan Hurt, Jul 07 2013]

MATHEMATICA

LinearRecurrence[{1, 0, 1, -1}, {1, 1, 4, 7}, 63] (* Jean-François Alcover, Jan 07 2019 *)

CROSSREFS

Cf. A080578.

Sequence in context: A131432 A088744 A168074 * A310931 A310932 A194121

Adjacent sequences: A061888 A061889 A061890 * A061892 A061893 A061894

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Benoit Cloitre, Apr 01 2003

STATUS

approved