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A221068 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX4 array.

%I A221068 #6 Jul 23 2025 01:40:29
%S A221068 16,56,4096,65536,829184,16777216,268435456,4185880576,68719476736,
%T A221068 1099511627776,17551735783424,281474976710656,4503599627370496,
%U A221068 72044225131708416,1152921504606846976,18446744073709551616
%N A221068 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their king-move neighbors in a random 0..3 nX4 array.
%C A221068 Column 4 of A221072
%H A221068 R. H. Hardin, <a href="/A221068/b221068.txt">Table of n, a(n) for n = 1..210</a>
%F A221068 Empirical: a(n) = 16*a(n-1) +1280*a(n-3) -20480*a(n-4) -726016*a(n-6) +11616256*a(n-7) +243236864*a(n-9) -3891789824*a(n-10) -54177169408*a(n-12) +866834710528*a(n-13) +8559911763968*a(n-15) -136958588223488*a(n-16) -999099251818496*a(n-18) +15985588029095936*a(n-19) +88516761267208192*a(n-21) -1416268180275331072*a(n-22) -6065057600834109440*a(n-24) +97040921613345751040*a(n-25) +325521958426885750784*a(n-27) -5208351334830172012544*a(n-28) -13798310784589052772352*a(n-30) +220772972553424844357632*a(n-31) +463933643691908201971712*a(n-33) -7422938299070531231547392*a(n-34) -12381420039132312466620416*a(n-36) +198102720626116999465926656*a(n-37) +261460839310197953740668928*a(n-39) -4183373428963167259850702848*a(n-40) -4335676130609162821497257984*a(n-42) +69370818089746605143956127744*a(n-43) +55704888638569365981756391424*a(n-45) -891278218217109855708102262784*a(n-46) -542593184231850628678886096896*a(n-48) +8681490947709610058862177550336*a(n-49) +3868852764963520870061692682240*a(n-51) -61901644239416333920987082915840*a(n-52) -19030852223934150966024236695552*a(n-54) +304493635582946415456387787128832*a(n-55) +57678102310384437768099995844608*a(n-57) -922849636966151004289599933513728*a(n-58) -81129638414606681695789005144064*a(n-60) +1298074214633706907132624082305024*a(n-61)
%e A221068 Some solutions for n=3
%e A221068 ..1..0..1..1....0..1..1..1....1..1..1..1....0..0..1..0....1..0..0..1
%e A221068 ..0..1..0..0....0..0..1..1....0..1..0..1....1..0..0..0....0..0..1..1
%e A221068 ..1..1..0..0....1..0..0..1....0..0..0..0....0..1..0..1....1..0..0..1
%K A221068 nonn
%O A221068 1,1
%A A221068 _R. H. Hardin_ Dec 31 2012