|
|
A141783
|
|
Number of bracelets (turn over necklaces) with n beads: 1 blue, 12 green, and r = n - 13 red.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
13,2
|
|
LINKS
|
|
|
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]
|
|
MAPLE
|
|
|
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Revised by Washington Bomfim, Jul 24 2012
|
|
STATUS
|
approved
|
|
|
|