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Number of 4Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors
1

%I #4 Nov 10 2013 05:37:01

%S 16,48,776,7697,70462,680302,6935963,69699237,689683944,6830674791,

%T 67982605070,676834294963,6729716953557,66892941751789,

%U 665135148008789,6614505307422976,65773605302169012,654010196878214180

%N Number of 4Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors

%C Row 4 of A231523

%H R. H. Hardin, <a href="/A231526/b231526.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) -23*a(n-2) +101*a(n-3) +734*a(n-4) -4730*a(n-5) -1987*a(n-6) -2442*a(n-7) -84415*a(n-8) +350229*a(n-9) +552203*a(n-10) -823403*a(n-11) +1850494*a(n-12) -4878983*a(n-13) -13339933*a(n-14) +14208703*a(n-15) -15634346*a(n-16) +32521122*a(n-17) +144142692*a(n-18) -108237346*a(n-19) +12655781*a(n-20) -18919194*a(n-21) -670476969*a(n-22) +140762199*a(n-23) +132252292*a(n-24) +19031686*a(n-25) +1208538437*a(n-26) +185768242*a(n-27) -177024291*a(n-28) -10977187*a(n-29) -706370171*a(n-30) -253074527*a(n-31) +35399416*a(n-32) +40637687*a(n-33) +185723061*a(n-34) +69289982*a(n-35) -27812168*a(n-36) -32459184*a(n-37) -15021208*a(n-38) -1420800*a(n-39) for n>40

%e Some solutions for n=5

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 10 2013