A116551 Permutation of natural numbers generated by 3-rowed array shown below.

0, 3, 1, 6, 4, 2, 9, 7, 5, 12, 10, 8, 15, 13, 11, 18, 16, 14, 21, 19, 17, 24, 22, 20, 27, 25, 23, 30, 28, 26, 33, 31, 29, 36, 34, 32, 39, 37, 35, 42, 40, 38, 45, 43, 41, 48, 46, 44, 51, 49, 47, 54, 52, 50, 57, 55, 53, 60, 58, 56, 63, 61, 59, 66, 64, 62, 69, 67, 65, 72, 70, 68, 75

Offset

1,2

Comments

0 3 6 9 12 15 18 21 24 ... a(n)= 3n

1 4 7 10 13 16 19 22 25 ... a(n)= 3n+1

2 5 8 11 14 17 20 23 26 ... a(n)= 3n+2

References

M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.

Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

Starting at the term a(3), a(n+3k) = a(n) + 3k, with k>=1.

From Chai Wah Wu, Jul 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 7.

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

Mathematica

Rest[CoefficientList[Series[x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1), {x, 0, 50}], x]] (* or *) Join[{0, 3, 1, 6, 4, 2, 9}, LinearRecurrence[{1, 0, 1, -1}, {7, 5, 12, 10}, 50]] (* G. C. Greubel, Sep 20 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1)) \\ G. C. Greubel, Sep 20 2017

Crossrefs

Cf. A115302.

Sequence in context: A209165 A121437 A078585 * A213783 A163330 A370394

Adjacent sequences: A116548 A116549 A116550 * A116552 A116553 A116554

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 17 2006

Status

approved