OFFSET
2,1
COMMENTS
Tarim's countdown: 2 people pass clubs to each other after n throws, then n-1 throws, then n-2, ..., 2, 1, 2, ... n-1. Thus for 3-countdown it is 3,2,1,2 (and repeat), or put in terms of pass throws and self-throws, pass-self-self-pass-self-pass-pass-self and repeat.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 2..1000
Martin Frost, An article in rec.juggling
Rob Street, An article in rec.juggling
Tarim, An article in rec.juggling
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
a(n) = n^2-1 for n odd, = 2(n^2-1) for n even.
a(n) = (3+(-1)^n)*(-1+n^2)/2. a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: 2*x^2*(x^4-6*x^2-4*x-3) / ((x-1)^3*(x+1)^3). - Colin Barker, Feb 18 2013
a(n) = LCM(2n+2, 2n-2). - Wesley Ivan Hurt, Jan 05 2014
a(n) = (n^2 - 1) * 2^(n+1 mod 2). - Wesley Ivan Hurt, Jan 05 2014
a(n) = (n+1) * (n-1) * (1 + ((n+1) mod 2)). - Wesley Ivan Hurt, Jan 05 2014
EXAMPLE
a(6) = 70 because 6^2 - 1 = 35 is odd, so it is doubled to 70 because the passing pattern must begin and end with same hand.
MAPLE
MATHEMATICA
Table[c=n^2-1; If[OddQ[n], c, 2c], {n, 2, 50}] (* Harvey P. Dale, Nov 27 2012 *)
PROG
(PARI) a(n)=if(n%2, 1, 2)*(n^2-1) \\ Charles R Greathouse IV, Feb 10 2017
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
Mark Tillotson (markt(AT)chaos.org.uk)
STATUS
approved