|
Search: id:A052515
|
|
|
| A052515 |
|
Number of pairs of sets of cardinality at least 2. |
|
+0
2
|
|
| 0, 0, 0, 0, 6, 20, 50, 112, 238, 492, 1002, 2024, 4070, 8164, 16354, 32736, 65502, 131036, 262106, 524248, 1048534, 2097108, 4194258, 8388560, 16777166, 33554380, 67108810, 134217672, 268435398, 536870852, 1073741762
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
a(n) is the number of binary sequences of length n having at least two 0's and at least two 1's. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 11 2009]
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 81
|
|
FORMULA
|
E.g.f.: exp(x)^2-2*exp(x)-2*x*exp(x)+1+2*x+x^2
Recurrence: {a(1)=0, (2*n+2)*a(n)+(-1-3*n)*a(n+1)+a(n+2)*n, a(2)=1/4*_C[0], a(3)=_C[0], a(4)=11/4*_C[0]+6}
For n>2, a(n) = 2^n - 2n - 2 = A005803(n) - 2 = A070313(n) - 1 = A071099(n) - A071099(n+1) + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 11 2004
|
|
EXAMPLE
|
a(4)=6 because there are six binary sequences of length four that have two or more 0's and two or more 1's: 0011,0101,0110,1100,1010,1001. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 11 2009]
|
|
MAPLE
|
Pairs spec := [S, {S=Prod(B, B), B=Set(Z, 2 <= card)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
lst={}; s=-1; Do[s+=s+n; AppendTo[lst, s], {n, 0, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 18 2008]
|
|
CROSSREFS
|
Sequence in context: A050768 A063488 A002415 this_sequence A067117 A119365 A001211
Adjacent sequences: A052512 A052513 A052514 this_sequence A052516 A052517 A052518
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 11 2004
|
|
|
Search completed in 0.002 seconds
|
