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Number of nX4 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Aug 07 2018 21:57:37

%S 1,3,4,7,34,56,77,228,551,1300,3171,6929,16038,38283,89884,210213,

%T 489040,1140562,2668604,6250857,14610077,34124180,79756933,186440331,

%U 435962650,1019155893,2382147016,5568392343,13017040048,30430709271,71136801083

%N Number of nX4 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 4 of A317815.

%H R. H. Hardin, <a href="/A317811/b317811.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) +8*a(n-5) -27*a(n-6) -20*a(n-7) -25*a(n-8) +70*a(n-9) +24*a(n-10) +124*a(n-11) +86*a(n-12) -80*a(n-13) -377*a(n-14) -343*a(n-15) -193*a(n-16) +448*a(n-17) +876*a(n-18) +779*a(n-19) -318*a(n-20) -936*a(n-21) -1187*a(n-22) -832*a(n-23) +863*a(n-24) +974*a(n-25) +1386*a(n-26) +118*a(n-27) -382*a(n-28) -1152*a(n-29) -661*a(n-30) +95*a(n-31) +336*a(n-32) +620*a(n-33) -201*a(n-34) +174*a(n-35) -269*a(n-36) +136*a(n-37) -152*a(n-38) +49*a(n-39) -76*a(n-40) +46*a(n-41) +11*a(n-42) -4*a(n-43) +16*a(n-44) -5*a(n-45) -a(n-48) for n>52

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A317815.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 07 2018