A208642 - OEIS

%I #9 Jul 05 2018 13:55:01

%S 64,610,2552,7548,18888,43284,94320,199299,412962,844943,1714680,

%T 3461238,6962956,13976742,28016664,56111133,112317270,224749641,

%U 449637728,899440872,1799078160,3598388200,7197048672,14394415431,28789200714

%N Number of 7 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

%C Row 7 of A208637.

%H R. H. Hardin, <a href="/A208642/b208642.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 50*a(n-3) - 55*a(n-4) + 36*a(n-5) - 13*a(n-6) + 2*a(n-7) for n>11.

%F Conjectures from _Colin Barker_, Jul 05 2018: (Start)

%F G.f.: x*(64 + 98*x - 600*x^2 + 402*x^3 + 428*x^4 - 378*x^5 - 144*x^6 + 77*x^7 + 78*x^8 - 8*x^9 - 16*x^10) / ((1 - x)^6*(1 - 2*x)).

%F a(n) = (51480*(-3+2^(1+n)) - 71394*n - 13145*n^2 - 1205*n^3 - 55*n^4 - n^5) / 120 for n>4.

%F (End)

%e Some solutions for n=4:

%e ..0..1..0..0....0..0..1..0....0..0..1..1....0..0..0..0....0..0..0..1

%e ..1..0..1..1....1..0..1..0....1..0..0..0....1..1..1..0....1..1..0..1

%e ..0..1..0..1....0..1..0..1....0..1..1..1....0..0..1..1....0..1..0..1

%e ..1..0..1..0....1..0..1..0....0..0..0..0....1..0..0..1....1..0..1..0

%e ..1..0..1..1....1..0..1..1....1..1..1..0....1..1..0..1....0..1..0..1

%e ..1..0..0..0....0..1..0..1....0..0..1..1....0..1..0..0....0..1..0..0

%e ..1..1..1..1....0..1..0..1....1..0..0..1....0..1..1..1....0..1..1..1

%Y Cf. A208637.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 29 2012