A004448 - OEIS

%I #39 Jul 07 2021 02:16:54

%S 7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,23,22,21,20,19,18,17,16,31,30,

%T 29,28,27,26,25,24,39,38,37,36,35,34,33,32,47,46,45,44,43,42,41,40,55,

%U 54,53,52,51,50,49,48,63,62,61,60,59,58,57,56,71,70,69,68,67,66,65,64,79,78,77,76,75,74,73,72,87,86,85

%N Nimsum n + 7.

%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 Vincenzo Librandi, <a href="/A004448/b004448.txt">Table of n, a(n) for n = 0..1000</a>

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

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F a(n) = n + (-1)^n + 2(-1)^floor(n/2) + 4(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005

%F G.f.: (8*x^8-x^7-x^6-x^5-x^4-x^3-x^2-x+7) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - _Colin Barker_, Jun 29 2014

%p A004448:=n->n+(-1)^n+2*(-1)^floor(n/2)+4*(-1)^floor(n/4): seq(A004448(n), n=0..100); # _Wesley Ivan Hurt_, Apr 28 2017

%t CoefficientList[Series[(8 x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x + 7)/((x - 1)^2 (x + 1) (x^2 + 1) (x^4 + 1)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 30 2014 *)

%o (PARI) Vec((8*x^8-x^7-x^6-x^5-x^4-x^3-x^2-x+7)/((x-1)^2*(x+1)*(x^2+1)*(x^4+1)) + O(x^100)) \\ _Colin Barker_, Jun 29 2014

%o (Python)

%o def a(n): return n^7

%o print([a(n) for n in range(83)]) # _Michael S. Branicky_, Jul 06 2021

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Jun 29 2014