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 (1,0,0,0,0,0,0,1,-1).
FORMULA
a(n) = n + (-1)^n + 2(-1)^floor(n/2) + 4(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005
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
MAPLE
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
MATHEMATICA
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 *)
PROG
(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
(Python)
def a(n): return n^7
print([a(n) for n in range(83)]) # Michael S. Branicky, Jul 06 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Jun 29 2014
STATUS
approved