OFFSET
1,2
COMMENTS
Column 2 of A185825.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..200
Robert Israel, Maple-assisted proof of formula
FORMULA
Empirical: a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5).
Empirical g.f.: x*(1 + 2*x - 2*x^2 - 11*x^3 - 20*x^4) / (1 - 7*x - 15*x^2 + 32*x^4 + 64*x^5). - Colin Barker, Apr 16 2018
Empirical formulas verified (see link). - Robert Israel, Jul 23 2018
EXAMPLE
Some solutions for 4 X 2 with a(1,1)=0:
..0..2....0..0....0..0....0..0....0..0....0..0....0..3....0..0....0..0....0..0
..0..2....1..1....0..0....0..3....3..2....2..0....0..3....3..4....0..2....0..3
..1..1....1..1....4..4....4..3....3..2....2..0....2..3....3..4....4..2....3..3
..0..0....0..0....3..3....4..3....3..3....1..1....2..2....3..4....4..2....2..2
MAPLE
f:= gfun:-rectoproc({a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5), a(1)=1, a(2)=9, a(3)=76, a(4)=656, a(5)=5680}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 23 2018
PROG
(PARI) x='x+O('x^99); Vec(x*(1+2*x-2*x^2-11*x^3-20*x^4)/(1-7*x-15*x^2+32*x^4+64*x^5)) \\ Altug Alkan, Jul 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 05 2011
STATUS
approved