OFFSET
0,1
COMMENTS
A self-inverse permutation of the natural numbers. - Philippe Deléham, Nov 22 2016
REFERENCES
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-1).
FORMULA
a(n) = n + 2*(-1)^floor(n/2) + 4*(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005
G.f.: (7*x^7 - 6*x^6 + 3*x^5 - 2*x^4 - x^3 + 2*x^2 - 5*x + 6)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)). - Colin Barker, Jun 29 2014
MATHEMATICA
CoefficientList[Series[(7 x^7 - 6 x^6 + 3 x^5 - 2 x^4 - x^3 + 2 x^2 - 5 x + 6)/((x - 1)^2 (x^2 + 1) (x^4 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 30 2014 *)
Table[BitXor[n, 6], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)
LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -1}, {6, 7, 4, 5, 2, 3, 0, 1}, 70] (* Harvey P. Dale, Sep 30 2017 *)
PROG
(PARI) Vec((7*x^7-6*x^6+3*x^5-2*x^4-x^3+2*x^2-5*x+6)/((x-1)^2*(x^2+1)*(x^4+1)) + O(x^100)) \\ Colin Barker, Jun 29 2014
(Magma) [BitwiseXor(n, 6): n in [0..70]]; // Bruno Berselli, Nov 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved