A206671 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.

1683, 9318, 57258, 319698, 1941084, 11368056, 70322310, 422623254, 2638207047, 16083282720, 100939297773, 620371263126, 3907034324082, 24124979612574, 152270113853484, 942768573570234, 5958426881684139, 36949316932383156

Offset

1,1

Comments

Column 3 of A206676.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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.

Example

Some solutions for n=4:
..2..1..0..2....1..2..1..1....1..2..2..2....2..0..0..0....1..0..1..1
..1..2..2..1....1..1..2..0....1..2..2..1....0..1..2..1....2..2..2..1
..1..2..2..1....1..1..2..1....2..1..1..2....1..1..0..0....0..2..2..0
..2..0..0..2....1..2..0..1....1..1..1..1....2..0..1..0....2..1..1..0
..1..0..0..2....2..0..0..2....2..0..2..0....0..0..2..2....2..1..1..2

Crossrefs

Sequence in context: A031539 A205739 A031719 * A205515 A335338 A263061

Adjacent sequences: A206668 A206669 A206670 * A206672 A206673 A206674

Keyword

nonn

Author

R. H. Hardin, Feb 11 2012

Status

approved