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%I #12 Dec 06 2017 03:42:47
%S 4,28,124,602,2776,12922,60720,286047,1335296,6256326,29377828,
%T 137595239,644951590,3024402309,14175895645,66459189937,311583082104,
%U 1460702584712,6848241858778,32106603868468,150524267596760,705711781367756
%N Number of nX2 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors
%C Column 2 of A231586
%H Robert Israel, <a href="/A231581/b231581.txt">Table of n, a(n) for n = 1..1488</a> (first 210 terms from R. H. Hardin)
%H Robert Israel, <a href="/A231581/a231581.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16).
%F Empirical formula verified by _Robert Israel_, Dec 06 2017 (see link).
%e Some solutions for n=7
%e ..0..0....3..0....2..1....0..3....2..0....2..3....2..2....1..1....3..3....0..0
%e ..0..2....0..0....1..1....0..0....0..0....2..2....0..0....2..1....0..0....0..1
%e ..1..0....0..0....0..0....0..1....1..0....3..2....0..0....1..2....0..0....0..0
%e ..0..0....0..2....0..0....0..2....0..0....1..1....1..3....0..0....0..3....3..0
%e ..2..0....0..1....0..2....0..0....0..1....1..1....0..0....0..0....0..0....0..1
%e ..2..0....0..0....2..0....0..0....0..0....1..1....0..0....0..0....3..0....0..0
%e ..0..0....0..0....0..0....2..0....3..0....2..1....2..3....0..2....0..0....0..3
%p rec:= a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16):
%p Data := [4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937]:
%p f:= gfun:-rectoproc({rec,seq(a(i)=Data[i],i=1..16)},a(n),remember):
%p map(f, [$1..40]); # _Robert Israel_, Dec 06 2017
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 11 2013
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