OFFSET
1,1
COMMENTS
From Noah Carey, Aug 31 2021: (Start)
Conjecture: a(n) is equal to half the sum along the edges of (centered, height 2, width n, starting at line n+1) rectangles in Pascal's triangle, as shown here for n=3 (not including the terms inside the rectangles):
1
1 1
1 2 1 a(3) = (4+6+4 + 15+20+15)/2
1 3 3 1
1 4---6---4 1
1 5 | | 5 1
1 6 15--20--15 6 1
1 7 21 35 35 20 7 1 (End)
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
Conjectures from Colin Barker, Mar 07 2018: (Start)
G.f.: x*(4 - 3*x) / ((1 - x)^2*(1 - 2*x)).
a(n) = 5*2^n - n - 5.
(End)
EXAMPLE
Some solutions for n=4:
0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0
1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 29 2012
STATUS
approved