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

Author

Giovanni Teofilatto, Mar 17 2006

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A115302.

Programs

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 *)

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

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)