A141783 Number of bracelets (turn over necklaces) with n beads: 1 blue, 12 green, and r = n - 13 red.

1, 7, 49, 231, 924, 3108, 9324, 25236, 63090, 147070, 323554, 676270, 1352540, 2600612, 4829708, 8692788, 15212379, 25949469, 43249115, 70562765, 112900424, 177412664, 274183208, 417232088, 625848132, 926250780, 1353751140

Offset: 13

Author

Washington Bomfim, Aug 17 2008

Keywords

• easy
• nonn

Links

• Harold S. Grant, On a Formula for Circular Permutations, Mathematics Magazine, Vol. 23, No. 3 (Jan. - Feb., 1950), pp. 133-136

Crossrefs

Cf. A005993, A005994, A005995, A018210, A018211, A018212, A018213, A018214, A002620, A062136.

Programs

Maple

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

Mathematica

Table[(1/2) (Binomial[n - 1, 12] + Binomial[(n - 2 + Mod[n, 2])/2, 6]), {n, 13, 50}] (* Wesley Ivan Hurt, Jan 30 2014 *)

Formula

a(n) = 1/2*(binomial(n-1,12) + binomial((n-2+n mod 2)/2, 6)).

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]

Extensions

Revised by Washington Bomfim, Jul 24 2012