login
A250271
Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.
1
3, 11, 27, 79, 255, 843, 2763, 8903, 28215, 88195, 272739, 836607, 2550735, 7742267, 23423355, 70695991, 213005415, 640982259, 1927141011, 5790335855, 17389881855, 52209491371, 156712360107, 470313240999, 1411308821655, 4234698216803
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5) for n>6.
Conjectures from Colin Barker, Nov 12 2018: (Start)
G.f.: x*(3 - 16*x + 21*x^2 + 24*x^3 - 60*x^4 + 24*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).
a(n) = 5*3^(n-1) - (2^n-2)*n for n>1.
(End)
EXAMPLE
Some solutions for n=6:
..0....0....2....0....0....2....2....0....2....2....2....1....2....2....1....0
..1....1....1....2....0....1....1....1....0....2....1....2....0....2....1....1
..1....2....1....2....1....2....2....1....0....2....0....2....0....2....1....2
..2....1....2....0....1....0....1....2....1....0....0....0....0....0....1....2
..2....2....0....0....1....2....2....0....0....2....0....1....1....2....2....2
..0....2....2....1....1....0....1....1....1....1....1....2....0....1....2....1
..2....0....2....2....2....2....2....2....0....2....2....1....2....0....1....0
CROSSREFS
Column 2 of A250277.
Sequence in context: A146826 A059400 A250223 * A289842 A077776 A113836
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 16 2014
STATUS
approved