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A231759 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

%I A231759 #6 Jul 23 2025 06:40:43
%S A231759 100,625,5041,40000,303601,2353156,18318400,141681409,1096603225,
%T A231759 8501393209,65862549769,510117350625,3952044600625,30617619155761,
%U A231759 237184671441601,1837438830737449,14234617914330724,110274092537986624
%N A231759 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.
%C A231759 Column 3 of A231764
%H A231759 R. H. Hardin, <a href="/A231759/b231759.txt">Table of n, a(n) for n = 1..210</a>
%F A231759 Empirical: a(n) = 4*a(n-1) +12*a(n-2) +149*a(n-3) +34*a(n-4) -745*a(n-5) -4377*a(n-6) -1298*a(n-7) +13107*a(n-8) +52121*a(n-9) +8083*a(n-10) -86996*a(n-11) -321488*a(n-12) -28134*a(n-13) +269200*a(n-14) +1028451*a(n-15) +72948*a(n-16) -507872*a(n-17) -2031587*a(n-18) -253166*a(n-19) +609639*a(n-20) +2548479*a(n-21) +414970*a(n-22) -482501*a(n-23) -2033465*a(n-24) -288069*a(n-25) +243904*a(n-26) +1017882*a(n-27) +103832*a(n-28) -88438*a(n-29) -327567*a(n-30) -19692*a(n-31) +23162*a(n-32) +69365*a(n-33) +1980*a(n-34) -4140*a(n-35) -9617*a(n-36) -152*a(n-37) +478*a(n-38) +849*a(n-39) +16*a(n-40) -33*a(n-41) -44*a(n-42) -a(n-43) +a(n-44) +a(n-45)
%e A231759 Some solutions for n=4
%e A231759 ..0..0..0..0....1..0..1..1....1..0..0..1....1..0..0..0....1..1..0..0
%e A231759 ..0..0..0..0....0..0..0..1....0..0..0..1....1..1..0..1....0..0..0..1
%e A231759 ..0..1..0..1....1..0..0..1....1..0..0..1....0..0..0..0....0..0..0..1
%e A231759 ..0..0..0..0....1..0..0..0....1..1..1..0....0..0..1..1....0..0..0..0
%e A231759 ..0..0..1..1....0..0..1..0....0..0..0..0....1..1..0..0....0..1..0..0
%K A231759 nonn
%O A231759 1,1
%A A231759 _R. H. Hardin_, Nov 13 2013