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Number of nX4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
1

%I #4 Dec 15 2017 21:14:28

%S 13,90,616,4543,32439,233636,1680927,12090311,86993766,625836038,

%T 4502532754,32392840662,233045620626,1676615590179,12062177118012,

%U 86779676209533,624324422549721,4491616025802673,32314312775187578

%N Number of nX4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.

%C Column 4 of A296578.

%H R. H. Hardin, <a href="/A296574/b296574.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +34*a(n-2) +86*a(n-3) -41*a(n-4) -205*a(n-5) +12*a(n-6) -945*a(n-7) -1071*a(n-8) +6854*a(n-9) -4693*a(n-10) -38024*a(n-11) +39526*a(n-12) +98155*a(n-13) -126589*a(n-14) -64284*a(n-15) +212215*a(n-16) -195549*a(n-17) +134699*a(n-18) +669038*a(n-19) -988888*a(n-20) -593854*a(n-21) +1633249*a(n-22) -105612*a(n-23) -1174790*a(n-24) +533435*a(n-25) +336787*a(n-26) -204805*a(n-27) -113690*a(n-28) -112779*a(n-29) +238970*a(n-30) -161545*a(n-31) -159003*a(n-32) +75189*a(n-33) -133398*a(n-34) -48052*a(n-35) -56319*a(n-36) -37620*a(n-37) -46453*a(n-38) +6538*a(n-39) -44560*a(n-40) +23243*a(n-41) -24495*a(n-42) +11317*a(n-43) -6722*a(n-44) +2439*a(n-45) -936*a(n-46) +257*a(n-47) -60*a(n-48) +12*a(n-49) -a(n-50)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A296578.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 15 2017