A131452 a(3n)=4n, a(3n+1)=4n+2, a(3n+2)=4n+1.

0, 2, 1, 4, 6, 5, 8, 10, 9, 12, 14, 13, 16, 18, 17, 20, 22, 21, 24, 26, 25, 28, 30, 29, 32, 34, 33, 36, 38, 37, 40, 42, 41, 44, 46, 45, 48, 50, 49, 52, 54, 53, 56, 58, 57, 60, 62, 61, 64, 66, 65, 68, 70, 69, 72, 74, 73, 76, 78, 77, 80, 82, 81, 84, 86, 85, 88, 90, 89, 92, 94, 93

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = (12*n-3+9*cos(2*(n-1)*Pi/3)-5*sqrt(3)*sin(2*(n-1)*Pi/3))/9. - Wesley Ivan Hurt, Sep 30 2017

G.f.: (x*(2 - x + 3*x^2))/((x - 1)^2*(1 + x + x^2)). - Georg Fischer, Nov 17 2022

Maple

nmax:= 40: gf:= (x*(2 - x + 3*x^2))/((x - 1)^2*(1 + x + x^2)): ser:= series(gf, x, nmax + 16): seq(coeff(ser, x, i), i=0..nmax); # Georg Fischer, Nov 17 2022

Mathematica

Table[Switch[Mod[n, 3], 0, 4 n/3, 1, 4 (n - 1)/3 + 2, 2, 4 (n - 2)/3 + 1], {n, 0, 71}] (* Michael De Vlieger, Sep 30 2017 *)

Crossrefs

Essentially partial sums of A131756.

Sequence in context: A036662 A134306 A006265 * A359898 A335920 A111104

Adjacent sequences: A131449 A131450 A131451 * A131453 A131454 A131455

Keyword

nonn,easy

Author

Paul Curtz, Oct 01 2007

Status

approved