A004451 - OEIS

%I #29 Sep 08 2022 08:44:33

%S 10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5,26,27,24,25,30,31,28,29,18,19,

%T 16,17,22,23,20,21,42,43,40,41,46,47,44,45,34,35,32,33,38,39,36,37,58,

%U 59,56,57,62,63,60,61,50,51

%N Nimsum n + 10.

%C A self-inverse permutation of the natural numbers. - _Philippe Deléham_, Nov 22 2016

%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.

%D J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.

%H <a href="/index/Ni#Nimsums">Index entries for sequences related to Nim-sums</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1,0,0,0,-1,2,-2,2,-1).

%F a(n) = n + 2(-1)^floor(n/2) + 8(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

%F G.f.: (11*x^11-10*x^10+7*x^9-6*x^8-5*x^3+6*x^2-9*x+10) / ((x-1)^2*(x^2+1)*(x^8+1)). - _Colin Barker_, Jun 29 2014

%p A004451:=n->n + 2*(-1)^floor(n/2) + 8*(-1)^floor(n/8); seq(A004451(n), n=0..50); # _Wesley Ivan Hurt_, Jun 29 2014

%t Table[n + 2 (-1)^Floor[n/2] + 8 (-1)^Floor[n/8], {n, 0, 50}] (* _Wesley Ivan Hurt_, Jun 29 2014 *)

%t LinearRecurrence[{2,-2,2,-1,0,0,0,-1,2,-2,2,-1},{10,11,8,9,14,15,12,13,2,3,0,1},100] (* _Harvey P. Dale_, Jul 02 2019 *)

%o (Magma) [n + 2*(-1)^Floor(n/2) + 8*(-1)^Floor(n/8) : n in [0..50]]; // _Wesley Ivan Hurt_, Jun 29 2014

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_