A249693 a(4n) = 3*n+1, a(2n+1) = 3*n+2, a(4n+2) = 3*n.

1, 2, 0, 5, 4, 8, 3, 11, 7, 14, 6, 17, 10, 20, 9, 23, 13, 26, 12, 29, 16, 32, 15, 35, 19, 38, 18, 41, 22, 44, 21, 47, 25, 50, 24, 53, 28, 56, 27, 59, 31, 62, 30, 65, 34, 68, 33, 71, 37, 74, 36, 77, 40, 80, 39, 83, 43, 86, 42, 89, 46, 92, 45

Offset: 0

Author

Paul Curtz, Dec 03 2014

Keywords

• nonn

Comments

A permutation of the nonnegative numbers.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Crossrefs

Cf. A001477, A010704, A010857, A016789, A061037.

Programs

Magma

m:=75; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6))); // G. C. Greubel, Sep 20 2018

Mathematica

a[n_] := (1/8)*(3*(-1)^(n+1)*(n+1)+9*n+10*{1, 0, -1, 0}[[Mod[n, 4]+1]]+1); Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 04 2014, after Robert Israel *)

PARI

x='x+O('x^75); Vec((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6)) \\ G. C. Greubel, Sep 20 2018

Formula

a(n+4) = a(n) + (sequence of period 2: repeat 3, 6).

a(4n+1) = 2*a(4n).

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).

a(n) is the rank of A061037(n) = -1, -3, 0, 5, ... in A247829(n) = 0, -1, -3, 2, ... .

G.f.: (1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6).

a(n) = (1 + 9*n - 3*(n+1)*(-1)^n + 10*cos(n*Pi/2))/8. - Robert Israel, Dec 03 2014