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A208641 Number of 6 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.

%I A208641 #11 Jul 22 2025 21:27:21
%S A208641 32,233,851,2331,5572,12404,26508,55260,113427,230559,465773,937321,
%T A208641 1881726,3772054,7554458,15121266,30257157,60531513,121083123,
%U A208641 242189591,484406152,968843304,1937722072,3875484536,7751014887,15502081539
%N A208641 Number of 6 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 A208641 Row 6 of A208637.
%H A208641 R. H. Hardin, <a href="/A208641/b208641.txt">Table of n, a(n) for n = 1..210</a>
%F A208641 Empirical: a(n) = 7*a(n-1) - 20*a(n-2) + 30*a(n-3) - 25*a(n-4) + 11*a(n-5) - 2*a(n-6) for n>9.
%F A208641 Conjectures from _Colin Barker_, Jul 05 2018: (Start)
%F A208641 G.f.: x*(32 + 9*x - 140*x^2 + 74*x^3 + 85*x^4 - 37*x^5 - 34*x^6 + 4*x^7 + 8*x^8) / ((1 - x)^5*(1 - 2*x)).
%F A208641 a(n) = (792*(7*2^n-10) - 3382*n - 539*n^2 - 38*n^3 - n^4) / 24 for n>3.
%F A208641 (End)
%e A208641 Some solutions for n=4:
%e A208641 ..0..1..0..1....0..0..0..1....0..0..0..1....0..0..0..0....0..1..0..1
%e A208641 ..0..1..0..0....1..1..0..1....1..1..0..0....1..1..1..0....0..1..0..0
%e A208641 ..0..1..1..0....0..1..0..1....0..1..1..0....0..0..1..1....1..0..1..0
%e A208641 ..0..0..1..0....0..1..0..0....0..0..1..1....1..0..0..1....0..1..0..1
%e A208641 ..1..0..1..1....0..1..1..1....1..0..0..1....1..1..0..1....1..0..1..0
%e A208641 ..1..0..0..0....1..0..0..0....1..1..0..0....0..1..0..0....1..0..1..1
%Y A208641 Cf. A208637.
%K A208641 nonn
%O A208641 1,1
%A A208641 _R. H. Hardin_, Feb 29 2012