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A039720 Period of n-countdown club-passing juggling pattern. 1
6, 8, 30, 24, 70, 48, 126, 80, 198, 120, 286, 168, 390, 224, 510, 288, 646, 360, 798, 440, 966, 528, 1150, 624, 1350, 728, 1566, 840, 1798, 960, 2046, 1088, 2310, 1224, 2590, 1368, 2886, 1520, 3198, 1680, 3526, 1848, 3870, 2024, 4230, 2208, 4606, 2400 (list; graph; refs; listen; history; text; internal format)
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

a(n) = A005563(n-1) * A000034(n-1). - 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

A039720:=n->(3+(-1)^n)*(n^2-1)/2; seq(A039720(n), n=2..100); # Wesley Ivan Hurt, Jan 05 2014

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

Sequence in context: A007829 A000773 A258283 * A056097 A099431 A323201

Adjacent sequences:  A039717 A039718 A039719 * A039721 A039722 A039723

KEYWORD

easy,nonn,nice

AUTHOR

Mark Tillotson (markt(AT)chaos.org.uk)

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)