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Number of nX7 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 neighbors
1

%I #5 Mar 31 2012 12:37:22

%S 64,1458,26772,459810,7702668,127750122,2110085532,34794255294,

%T 573347277990,9445146465474,155579502783600,2562580517033736,

%U 42208064346447486,695201252701136796,11450503035670908312

%N Number of nX7 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 neighbors

%C Column 7 of A208314

%H R. H. Hardin, <a href="/A208313/b208313.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 65*a(n-1) -1953*a(n-2) +36966*a(n-3) -502122*a(n-4) +5256909*a(n-5) -44318169*a(n-6) +309490947*a(n-7) -1823975982*a(n-8) +9183492558*a(n-9) -39813195762*a(n-10) +149339766420*a(n-11) -486017305326*a(n-12) +1374228095598*a(n-13) -3377800131066*a(n-14) +7218074976993*a(n-15) -13409006027409*a(n-16) +21654224930979*a(n-17) -30400201179594*a(n-18) +37104158581146*a(n-19) -39367401731406*a(n-20) +36289563240060*a(n-21) -29023819710498*a(n-22) +20084298224346*a(n-23) -11967106417902*a(n-24) +6091710309801*a(n-25) -2616943561281*a(n-26) +931245658623*a(n-27) -266848217802*a(n-28) +58935744018*a(n-29) -9341138457*a(n-30) +932678955*a(n-31) -43046721*a(n-32)

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 25 2012