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A207700 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207700 #12 Jun 25 2018 08:54:50
%S A207700 15,225,1071,3321,8151,17225,32775,57681,95551,150801,228735,335625,
%T A207700 478791,666681,908951,1216545,1601775,2078401,2661711,3368601,4217655,
%U A207700 5229225,6425511,7830641,9470751,11374065,13570975,16094121,18978471
%N A207700 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207700 Column 5 of A207703.
%H A207700 R. H. Hardin, <a href="/A207700/b207700.txt">Table of n, a(n) for n = 1..210</a>
%F A207700 Empirical: a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A207700 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207700 G.f.: x*(15 + 135*x - 54*x^2 - 30*x^3 + 15*x^4 - x^5) / (1 - x)^6.
%F A207700 a(n) = (3 - 10*n - 15*n^2 + 44*n^3 + 21*n^4 + 2*n^5) / 3.
%F A207700 (End)
%e A207700 Some solutions for n=4:
%e A207700 ..1..0..0..1..1....0..0..1..1..1....0..0..1..1..0....1..1..0..1..1
%e A207700 ..0..1..1..0..1....0..1..1..0..1....0..0..1..1..0....1..1..0..1..1
%e A207700 ..1..1..1..0..1....0..0..1..1..1....0..0..1..1..0....1..1..0..1..1
%e A207700 ..1..1..1..0..1....0..0..1..1..1....0..0..1..1..0....1..1..0..1..1
%Y A207700 Cf. A207703.
%K A207700 nonn
%O A207700 1,1
%A A207700 _R. H. Hardin_, Feb 19 2012