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Number of (3+1)X(n+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
1

%I #6 Nov 22 2013 09:09:13

%S 13,115,1202,14042,164014,1905436,22161823,257723189,2997153100,

%T 34854893113,405339144562,4713824245681,54818634195843,

%U 637504183234586,7413748797343868,86216957745461401,1002645760786026294

%N Number of (3+1)X(n+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero

%C Row 3 of A232316

%H R. H. Hardin, <a href="/A232319/b232319.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) +31*a(n-2) -109*a(n-3) -423*a(n-4) +475*a(n-5) +2814*a(n-6) -563*a(n-7) -11261*a(n-8) -3072*a(n-9) +29843*a(n-10) +16787*a(n-11) -54209*a(n-12) -43221*a(n-13) +65550*a(n-14) +74635*a(n-15) -48250*a(n-16) -90588*a(n-17) +14301*a(n-18) +74590*a(n-19) +8049*a(n-20) -40363*a(n-21) -5412*a(n-22) +7933*a(n-23) +1763*a(n-24) +602*a(n-25) +322*a(n-26) -29*a(n-27) -378*a(n-28) -22*a(n-29) +42*a(n-30) +12*a(n-31) -4*a(n-32) for n>34

%e Some solutions for n=5

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2013