A113655 Reverse blocks of three in the sequence of natural numbers.

3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 18, 17, 16, 21, 20, 19, 24, 23, 22, 27, 26, 25, 30, 29, 28, 33, 32, 31, 36, 35, 34, 39, 38, 37, 42, 41, 40, 45, 44, 43, 48, 47, 46, 51, 50, 49, 54, 53, 52, 57, 56, 55, 60, 59, 58, 63, 62, 61, 66, 65, 64, 69, 68, 67, 72, 71, 70

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 3*floor((n+2)/3) - (n-1) mod 3. - Robert G. Wilson v and Zak Seidov, Jan 20 2006

a(n) = a(n-3)+3 = a(n-1)+a(n-3)-a(n-4). - Jaume Oliver Lafont, Dec 02 2008

G.f.: (3*x - x^2 - x^3 + 2*x^4)/(1 - x - x^3 + x^4) = x*(3 - x - x^2 + 2*x^3)/((1 + x + x^2)*(1-x)^2). - Jaume Oliver Lafont, Mar 25 2009

a(n) = 6*floor((n+2)/3) - n - 2. - Dennis P. Walsh, Aug 16 2013

a(n) = A000027(n) + 2 * A057078(n+2). - Dennis P. Walsh, Aug 16 2013

a(n) = n + 2 * A079918(n-1) - 2 * A079918(n). - Dennis P. Walsh, Aug 16 2013

a(n) = n - 2*A049347(n). - Wesley Ivan Hurt, Sep 27 2017, simplified Jun 30 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2). - Amiram Eldar, Jan 31 2023

Maple

seq(6*floor((n+2)/3)-n-2, n=1..72); # Dennis P. Walsh, Aug 16 2013

Mathematica

f[n_] := Switch[ Mod[n, 3], 0, n - 2, 1, n + 2, 2, n]; Array[f, 72] (* Robert G. Wilson v, Jan 18 2006 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 2, 1, 6}, 100] (* or *) CoefficientList[Series[(3 - x - x^2 + 2 x^3) / ((1 + x + x^2) (1 - x)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 28 2017 *)
Reverse/@Partition[Range[81], 3]//Flatten (* Harvey P. Dale, Oct 11 2020 *)

Prog

(PARI) a(n)=2+n-2*((n+2)%3); \\ Jaume Oliver Lafont, Mar 25 2009
(Magma) I:=[3, 2, 1, 6]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..80]]; // Vincenzo Librandi, Sep 28 2017

Crossrefs

Cf. A000027, A049347, A057078, A079918.

Sequence in context: A120771 A115094 A165958 * A177977 A365743 A208520

Adjacent sequences: A113652 A113653 A113654 * A113656 A113657 A113658

Keyword

nonn,easy

Author

Parag D. Mehta (pmehta23(AT)gmail.com), Jan 16 2006

Extensions

More terms from Robert G. Wilson v, Jan 18 2006

Status

approved