A116080 Permutation of natural numbers generated by 4-rowed array shown below.

0, 4, 1, 8, 5, 2, 12, 9, 6, 3, 16, 13, 10, 7, 20, 17, 14, 11, 24, 21, 18, 15, 28, 25, 22, 19, 32, 29, 26, 23, 36, 33, 30, 27, 40, 37, 34, 31, 44, 41, 38, 35, 48, 45, 42, 39, 52, 49, 46, 43, 56, 53, 50, 47, 60, 57, 54, 51, 64, 61, 58, 55, 68, 65, 62, 59, 72, 69, 66, 63, 76, 73, 70

Offset: 1

Author

Giovanni Teofilatto, Mar 12 2006

Keywords

• easy
• nonn

Comments

0 4 8 12 16 20 24 28 32 ... a(n) = 4n => A008586;

1 5 9 13 17 21 25 29 33 ... a(n) = 4n+1 => A016813;

2 6 10 14 18 22 26 30 34 ... a(n) = 4n+2 => A016825;

3 7 11 15 19 23 27 31 35 ... a(n) = 4n+3 => A004767.

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

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1).

Crossrefs

Cf. A115302.

Programs

Mathematica

LinearRecurrence[{1,0,0,1,-1},{0,4,1,8,5,2,12,9,6,3,16},80] (* Harvey P. Dale, Feb 20 2022 *)

Formula

For n > 0, a(n+5) = a(n) + 8 iff a(n+5)= 1.

a(n)= a(n-1) + a(n-4) - a(n-5), n>=12. - R. J. Mathar, Apr 22 2010

G.f.: x^2*(4-3*x+7*x^2-3*x^3-7*x^4+13*x^5-10*x^6+3*x^9)/(1-x-x^4+x^5). - Philippe Deléham, Dec 02 2016

Extensions

Corrected (47 replaced by 41) by R. J. Mathar, Apr 22 2010