OFFSET
1,1
COMMENTS
Column 3 of A181217.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..300
Robert Israel, Maple-assisted proof of formula
Index entries for linear recurrences with constant coefficients, signature (6,0,16, 21,-78,-32,0,-12,8).
FORMULA
Empirical: a(n) = 6*a(n-1) + 16*a(n-3) + 21*a(n-4) - 78*a(n-5) - 32*a(n-6) - 12*a(n-8) + 8*a(n-9).
Empirical g.f.: 4*x*(2 + 4*x + 4*x^2 - 7*x^3 - 23*x^4 - 9*x^5 - x^6 - 2*x^7 + 2*x^8) / ((1 - 6*x - 3*x^2 + 2*x^3)*(1 + 3*x^2 - 12*x^4 - 4*x^6)). - Colin Barker, Feb 22 2018
Empirical formula confirmed by Robert Israel, Apr 30 2018: see link.
EXAMPLE
Some avoided solutions for 4 X 3:
0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1
0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0
1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1
MAPLE
f:= gfun:-rectoproc({a(n) = 6*a(n-1) + 16*a(n-3) + 21*a(n-4) - 78*a(n-5) - 32*a(n-6) - 12*a(n-8) + 8*a(n-9), seq(a(i)=[8, 64, 400, 2500, 16100, 103684, 665252, 4268356, 27399292][i], i=1..9)}, a(n), remember):
map(f, [$1..20]); # Robert Israel, Apr 30 2018
MATHEMATICA
LinearRecurrence[{6, 0, 16, 21, -78, -32, 0, -12, 8}, {8, 64, 400, 2500, 16100, 103684, 665252, 4268356, 27399292}, 20] (* Vincenzo Librandi, May 01 2018 *)
PROG
(Magma) I:=[8, 64, 400, 2500, 16100, 103684, 665252, 4268356, 27399292]; [n le 9 select I[n] else 6*Self(n-1)+16*Self(n-3)+21*Self(n-4)-78*Self(n-5) -32*Self(n-6)-12*Self(n-8)+8*Self(n-9): n in [1..25]]; // Vincenzo Librandi, May 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 10 2010
STATUS
approved