OFFSET
1,1
COMMENTS
Column 5 of A209650.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of formula
FORMULA
Empirical: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n.
Conjectures from Colin Barker, Mar 07 2018: (Start)
G.f.: 14*x*(1 + 9*x - 3*x^2 - x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
Empirical formula (and thus Barker's conjectures) proved by Robert Israel, Mar 07 2018: see link.
EXAMPLE
Some solutions for n=4:
0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0
1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1
1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
MAPLE
seq(7/2*n^4+21*n^3-7/2*n^2-7*n, n=1..50); # Robert Israel, Mar 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2012
STATUS
approved