|
|
A224543
|
|
Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent.
|
|
1
|
|
|
8, 32, 78, 196, 428, 916, 1858, 3678, 7096, 13458, 25150, 46466, 85028, 154356, 278298, 498792, 889320, 1578248, 2789166, 4910498, 8615348, 15067462, 26274538, 45693286
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9).
Empirical g.f.: 2*x*(4 - 8*x - 9*x^2 + 36*x^3 - 34*x^4 + 11*x^5 - 5*x^6 + 7*x^7 + x^8) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Aug 30 2018
|
|
EXAMPLE
|
Some solutions for n=3:
..0..1..0..0....0..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0
..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..1..1..1
..0..1..0..1....0..0..0..0....0..0..0..1....1..1..1..1....0..0..0..0
..0..1..0..1....0..1..1..1....0..0..0..1....0..0..0..0....0..1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|