A115731 Permutation of natural numbers generated by 3-rowed array shown below.

1, 6, 2, 7, 5, 3, 12, 8, 4, 13, 11, 9, 18, 14, 10, 19, 17, 15, 24, 20, 16, 25, 23, 21, 30, 26, 22, 31, 29, 27, 36, 32, 28, 37, 35, 33, 42, 38, 34, 43, 41, 39, 48, 44, 40, 49, 47, 45, 54, 50, 46, 55, 53, 51, 60, 56, 52, 61, 59, 57, 66, 62, 58, 67, 65, 63, 72, 68, 64, 73, 71, 69

Offset: 1

Author

Giovanni Teofilatto, Mar 19 2006

Keywords

• easy
• nonn

Comments

1 6 7 12 13 18 19 24 25 ... a(n)=congruent to {0, 1} mod 6, Cf. A047225.

2 5 8 11 14 17 20 23 26 ... a(n)= 3n+2= A016789.

3 4 9 10 15 16 21 22 27 ... a(n)=congruent to {3, 4} mod 6, Cf. A047230.

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

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Crossrefs

Cf. A115302.

Programs

PARI

Vec(x*(1 + 4*x - 8*x^2 + 13*x^3 - 15*x^4 + 13*x^5 - 5*x^6 - 4*x^7 + 4*x^8) / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Apr 01 2018

Formula

Starting with the term a(3), a(n+6k) = a(n) + 6k, with k>=1.

From Colin Barker, Apr 01 2018: (Start)

G.f.: x*(1 + 4*x - 8*x^2 + 13*x^3 - 15*x^4 + 13*x^5 - 5*x^6 - 4*x^7 + 4*x^8) / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) for n>9.

(End)