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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: A345003 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 August 10 11:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)