Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Dec 13 2015 21:16:37
%S 1683,9318,57258,319698,1941084,11368056,70322310,422623254,
%T 2638207047,16083282720,100939297773,620371263126,3907034324082,
%U 24124979612574,152270113853484,942768573570234,5958426881684139,36949316932383156
%N Number of (n+1) X 4 0..2 arrays with no 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors or the same number of counterclockwise edge increases as its vertical neighbors.
%C Column 3 of A206676.
%H R. H. Hardin, <a href="/A206671/b206671.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 77*a(n-2) +10*a(n-3) -1922*a(n-4) -516*a(n-5) +19793*a(n-6) +5428*a(n-7) -113120*a(n-8) -3934*a(n-9) +514201*a(n-10) -98474*a(n-11) +674498*a(n-12) +2473984*a(n-13) -4594788*a(n-14) -9363346*a(n-15) -39894849*a(n-16) -6685462*a(n-17) +103265036*a(n-18) +113942422*a(n-19) +182404120*a(n-20) -261065134*a(n-21) -428184903*a(n-22) -1235480160*a(n-23) +140418119*a(n-24) +707211400*a(n-25) -380022979*a(n-26) +8501554228*a(n-27) -1359074284*a(n-28) +10770977422*a(n-29) -3374740807*a(n-30) -1727398374*a(n-31) +6854827606*a(n-32) -22609828262*a(n-33) +18528663308*a(n-34) -33973029042*a(n-35) +13867319793*a(n-36) -13750932690*a(n-37) -14590281557*a(n-38) +34128066012*a(n-39) -46983330873*a(n-40) +75599422758*a(n-41) -71541999131*a(n-42) +82677241590*a(n-43) -76468990762*a(n-44) +74991177258*a(n-45) -73059755289*a(n-46) +62152219882*a(n-47) -58660945862*a(n-48) +47019559864*a(n-49) -42094966520*a(n-50) +33953138780*a(n-51) -26881309568*a(n-52) +22155542128*a(n-53) -12958164074*a(n-54) +6711583328*a(n-55) -1188948418*a(n-56) -990321576*a(n-57) +474320708*a(n-58) -101614000*a(n-59) -276473616*a(n-60) +404974400*a(n-61) -178150784*a(n-62) +29632000*a(n-63) -14858240*a(n-64) +4571136*a(n-65) -698368*a(n-66) +614400*a(n-67) +49152*a(n-68) +65536*a(n-69) for n>70.
%e Some solutions for n=4:
%e ..2..1..0..2....1..2..1..1....1..2..2..2....2..0..0..0....1..0..1..1
%e ..1..2..2..1....1..1..2..0....1..2..2..1....0..1..2..1....2..2..2..1
%e ..1..2..2..1....1..1..2..1....2..1..1..2....1..1..0..0....0..2..2..0
%e ..2..0..0..2....1..2..0..1....1..1..1..1....2..0..1..0....2..1..1..0
%e ..1..0..0..2....2..0..0..2....2..0..2..0....0..0..2..2....2..1..1..2
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 11 2012