A115659 - OEIS

%I #28 Jun 17 2024 14:23:21

%S 0,3,1,4,2,7,5,8,6,11,9,12,10,15,13,16,14,19,17,20,18,23,21,24,22,27,

%T 25,28,26,31,29,32,30,35,33,36,34,39,37,40,38,43,41,44,42,47,45,48,46,

%U 51,49,52,50,55,53,56,54,59,57,60,58,63,61,64,62

%N Permutation of natural numbers generated by 2-rowed array shown below.

%C 0 3 4 7 8 11 12 15 ...: integers congruent to 0 or 3 mod 4.

%C 1 2 5 6 9 10 13 14 ...: integers congruent to 1 or 2 mod 4.

%C Essentially the same as A067060. - _Hugo Pfoertner_, Jun 16 2024

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

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F For n>0, a(n+4k) = a(n) + 4k, with k>=0.

%F G.f.: x^2*(3 - 2*x + 3*x^2 - 2*x^3 + 2*x^4)/(1 - x - x^4 + x^5). - _Philippe Deléham_, Dec 02 2016

%t Join[{0}, LinearRecurrence[{1, 0, 0, 1, -1}, {3, 1, 4, 2, 7}, 70]] (* _Vincenzo Librandi_, Dec 02 2016 *)

%o (Magma) I:=[0, 3, 1, 4, 2, 7]; [n le 6 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, Dec 02 2016

%Y Cf. A067060, A090964, A116468.

%K easy,nonn

%O 1,2

%A _Giovanni Teofilatto_, Mar 18 2006

%E Entries corrected by _R. J. Mathar_, Oct 25 2011