A109362 Period 6: repeat [0, 0, 1, 2, 0, 3].

0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2, 0, 3, 0, 0, 1, 2

Offset

0,4

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1em[I]sumseq[ - .25'i - .5'j - .25i' - .5j' + .25'ii' + .25'jj' - .75'kk' + .25'jk' + .25'kj' + .25e]; sumtype: (Y[15], *, sum)

Links

Table of n, a(n) for n=0..81.

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

Formula

G.f.: x^2*(1 + 2*x + 3*x^3)/((1 - x)*(x + 1)*(x^2 + x + 1)*(x^2 - x + 1)). [corrected by Georg Fischer, May 15 2019]

a(n) = (3 - cos(n*Pi/3) - 2*cos(n*Pi) - sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3)) / 3. - Wesley Ivan Hurt, Apr 26 2020

Mathematica

PadRight[{}, 100, {0, 0, 1, 2, 0, 3}] (* or *)
LinearRecurrence[{0, 0, 0, 0, 0, 1}, {0, 0, 1, 2, 0, 3}, 100] (* Georg Fischer, May 15 2019 *)

Prog

(PARI) a(n)=[0, 0, 1, 2, 0, 3][n%6+1]; \\ Georg Fischer, May 15 2019

Crossrefs

Sequence in context: A261727 A234579 A309332 * A085246 A268726 A035182

Adjacent sequences: A109359 A109360 A109361 * A109363 A109364 A109365

Keyword

nonn,easy

Author

Creighton Dement, Aug 22 2005

Status

approved