|
|
A212407
|
|
Number of binary arrays of length 2*n+5 with no more than n ones in any length 2n subsequence (=50% duty cycle).
|
|
1
|
|
|
34, 166, 747, 3179, 13185, 54042, 220054, 892387, 3609005, 14567294, 58714842, 236397086, 950965002, 3822869204, 15359318444, 61681353571, 247609729669, 993662549686, 3986465243314, 15989373858826, 64118439206974
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical (for n>=5): n*(181*n^2 - 792*n + 581)*a(n) = 2*(724*n^3 - 3711*n^2 + 4112*n + 210)*a(n-1) - 8*(2*n-7)*(181*n^2 - 430*n - 30)*a(n-2). - Vaclav Kotesovec, Nov 20 2012
Empirical (for n>=3): a(n) = 4^(n+2) - 2*(181*n^2 - 264*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - Vaclav Kotesovec, Nov 20 2012
|
|
EXAMPLE
|
Some solutions for n=3:
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1
0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0
1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0
0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0
1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0
0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0
0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1
0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0
1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1
|
|
MAPLE
|
#verified first terms (holds for all n<=210).
with(gfun): A212407:= rectoproc({a(3)=747, a(4)=3179, n*(181*n^2-792*n+581)*a(n) = 2*(724*n^3-3711*n^2+4112*n+210)*a(n-1) - 8*(2*n-7)*(181*n^2-430*n-30)*a(n-2)}, a(n), remember): 34, 166, seq(A212407(n), n=3..20); A212407(210); # Vaclav Kotesovec, Nov 20 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|