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%I #17 Jan 31 2014 09:55:40
%S 1,7,49,231,924,3108,9324,25236,63090,147070,323554,676270,1352540,
%T 2600612,4829708,8692788,15212379,25949469,43249115,70562765,
%U 112900424,177412664,274183208,417232088,625848132,926250780,1353751140
%N Number of bracelets (turn over necklaces) with n beads: 1 blue, 12 green, and r = n - 13 red.
%H Harold S. Grant, <a href="http://www.jstor.org/pss/3029277">On a Formula for Circular Permutations</a>, Mathematics Magazine, Vol. 23, No. 3 (Jan. - Feb., 1950), pp. 133-136
%F a(n) = 1/2*(binomial(n-1,12) + binomial((n-2+n mod 2)/2, 6)).
%F a(n) = (1/(2*12!))*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*((n+1)*(n+3)*(n+5)*(n+7)*(n+9)*(n+11) + 1*3*5*7*9*11) - (1/15)*(1/2^10)*(n^5+(65/2)*n^4+400*n^3+(4615/2)*n^2+6154*n+(11895/2))*(1/2)*(1-(-1)^n) [_Yosu Yurramendi_, Jun 24 2013]
%p A141783:=n->(1/2)*(binomial(n - 1, 12) + binomial((n - 2 + (n mod 2))/2, 6)); seq(A141783(n), n=13..50); # _Wesley Ivan Hurt_, Jan 30 2014
%t Table[(1/2) (Binomial[n - 1, 12] + Binomial[(n - 2 + Mod[n, 2])/2, 6]), {n, 13, 50}] (* _Wesley Ivan Hurt_, Jan 30 2014 *)
%Y Cf. A005993, A005994, A005995, A018210, A018211, A018212, A018213, A018214, A002620, A062136.
%K easy,nonn
%O 13,2
%A _Washington Bomfim_, Aug 17 2008
%E Revised by Washington Bomfim, Jul 24 2012
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