A231460 - OEIS

%I #4 Nov 09 2013 07:26:53

%S 33,90,311,1096,4138,16384,67189,280852,1195147,5145988,22393436,

%T 98203218,433447413,1922772634,8563359553,38258390042,171345914564,

%U 768880010838,3455375274145,15546790384874,70013535581867

%N Number of (n+1)X(4+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%C Column 4 of A231463

%H R. H. Hardin, <a href="/A231460/b231460.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) -29*a(n-2) -61*a(n-3) +274*a(n-4) +278*a(n-5) -1193*a(n-6) -1403*a(n-7) +1527*a(n-8) +8863*a(n-9) +3480*a(n-10) -36412*a(n-11) -703*a(n-12) +39337*a(n-13) +59413*a(n-14) -61219*a(n-15) -144858*a(n-16) +71992*a(n-17) +173024*a(n-18) +42768*a(n-19) -298824*a(n-20) +457904*a(n-21) -1004901*a(n-22) +921771*a(n-23) +511731*a(n-24) -1585969*a(n-25) +1962186*a(n-26) -2663476*a(n-27) +2120499*a(n-28) -668261*a(n-29) -214674*a(n-30) +1074212*a(n-31) -2169000*a(n-32) +2007268*a(n-33) -1259600*a(n-34) +1089544*a(n-35) -214867*a(n-36) -230041*a(n-37) +306189*a(n-38) -289905*a(n-39) +194165*a(n-40) -200257*a(n-41) +43085*a(n-42) -37027*a(n-43) -26660*a(n-44) -1262*a(n-45) -665*a(n-46) +14067*a(n-47) +566*a(n-48) +4354*a(n-49) +1920*a(n-50) +1320*a(n-51) -480*a(n-52) for n>55

%e Some solutions for n=5

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

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

%e ..2..2..1..1..1....0..1..1..1..1....2..2..1..1..1....0..0..0..1..1

%e ..2..2..2..1..1....0..0..1..1..1....2..2..2..1..1....0..0..1..1..1

%e ..2..2..3..3..3....0..0..0..1..1....2..2..3..3..3....0..0..0..1..1

%e ..3..3..3..3..3....0..0..0..0..0....3..3..3..3..3....0..0..0..0..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2013