|
|
A272352
|
|
a(n) is the number of ways of putting n labeled balls into 2 indistinguishable boxes such that each box contains at least 3 balls.
|
|
6
|
|
|
10, 35, 91, 210, 456, 957, 1969, 4004, 8086, 16263, 32631, 65382, 130900, 261953, 524077, 1048344, 2096898, 4194027, 8388307, 16776890, 33554080, 67108485, 134217321, 268435020, 536870446, 1073741327, 2147483119, 4294966734, 8589933996, 17179868553
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
6,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^6*(10 - 15*x + 6*x^2)/((1 - x)^3*(1 - 2*x)).
a(n) = (2^n - 2 - 2*n - 2*binomial(n, 2))/2.
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4), for n > 3.
|
|
EXAMPLE
|
For n=6, label the balls A, B, C, D, E, and F. Then each box must contain exactly 3 balls, and the 10 ways are ABC/DEF, ABD/CEF, ABE/CDF, ABF/CDE, ACD/BEF, ACE/BDF, ACF/BDE, ADE/BCF, ADF/BCE, AEF/BCD. - Michael B. Porter, Jul 01 2016
|
|
MATHEMATICA
|
Table[1/2 (2^n - 2 - 2 n - 2 Binomial[n, 2]), {n, 6, 40}]
LinearRecurrence[{5, -9, 7, -2}, {10, 35, 91, 210}, 30] (* Harvey P. Dale, Mar 29 2018 *)
|
|
PROG
|
(Magma) [(2^n-2-2*n-2*Binomial(n, 2))/2: n in [6..50]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|