OFFSET
0,4
COMMENTS
Created to simplify the definition of A129952.
a(n) = abs(A009531(n-1)).
Starting (1, 2, 1, 4,...): square (1 + x - x^2 - x^3 + x^4 + x^5 - ...) = (1 + 2x - x^2 - 4x^3 + x^4 + 6x^5 - ...).
With a(3) taken as 0, a(n+2) = n^k+1 mod 2*n, n>=1, for any k>=2, also for k=n. - Wolfdieter Lang, Dec 21 2011
Also !(n+2) mod n for n>0 where !n is a subfactorial number (A000166). - Michel Lagneau, Sep 05 2012
Greatest common divisor of n-1 and (n-1) mod 2. - Bruno Berselli, Mar 07 2017
REFERENCES
Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(n) = 1 for even n, a(n) = n-1 for odd n.
a(2*k) = 1, a(2*k+1) = 2*k.
G.f.: (1 - x^2 + 2*x^3)/((1 - x)^2*(1 + x)^2).
a(n) = (n - (n - 2)*(-1)^n)/2. - Bruno Berselli, May 06 2011
E.g.f.: 1 + x^2*U(0)/2 where U(k)= 1 + 2*x*(k+1)/(2*k + 3 - x*(2*k+3)/(x + 4*(k+2)*(k+1)/U(k+1)) (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Oct 20 2012
a(n) = 2*floor(n/2) - (n-1)*((n-1) mod 2). - Wesley Ivan Hurt, Oct 19 2013
a(n) = (n-1)^((1-(-1)^n)/2). - Wesley Ivan Hurt, Mar 21 2015
a(n) = (n-1) - a(a(n-1))*a(n-1), a(0) = 0. - Eli Jaffe, Jun 07 2016
E.g.f.: (x + 1)*cosh(x) - sinh(x). - Ilya Gutkovskiy, Jun 07 2016
a(n) = (-1)^n mod n for n > 0. - Franz Vrabec, Mar 06 2020
a(n) = (n-1)^(n mod 2). - Karl V. Keller, Jr., Aug 01 2020
MAPLE
MATHEMATICA
Join[{1}, Riffle[2Range[0, 50], 1]] (* Harvey P. Dale, Nov 02 2011 *)
PROG
(PARI) {for(n=0, 85, print1(if(n%2>0, n-1, 1), ", "))}
(Magma) &cat[[1, 2*k]: k in [0..42]];
(Python) print([(n-1)**(n%2) for n in range(0, 86)]) # Karl V. Keller, Jr., Jul 26 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 13 2007
EXTENSIONS
More terms from Klaus Brockhaus, Jun 16 2007
Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar
STATUS
approved