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

1,2

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).

Formula

For n > 0, a(n+5) = a(n) + 8 iff a(n+5)<a(n) : a(n+7) = a(n) + 8, iff a(n+7)<a(n): a(n+4k) = a(n) + 4k with k >= 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

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 *)

Crossrefs

Cf. A115302.

Sequence in context: A141567 A254707 A134417 * A343125 A205296 A143820

Adjacent sequences: A116077 A116078 A116079 * A116081 A116082 A116083

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 12 2006

Extensions

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

Status

approved