A207231 Number of nX4 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row, column, diagonal or antidiagonal

61, 3721, 79353, 2464241, 77937497, 2320163321, 68168506265, 2020945709121, 60380821140105, 1805255994953521, 53870184420454537, 1606029526149186945, 47888299964589797753, 1428391142485388208081, 42609054655547072314217

Offset

1,1

Comments

Column 4 of A207235

Links

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

Formula

Empirical: a(n) = 41*a(n-1) -496*a(n-2) +4331*a(n-3) +27801*a(n-4) -226424*a(n-5) -4051830*a(n-6) -3843930*a(n-7) +81577316*a(n-8) -230470928*a(n-9) +4929482616*a(n-10) +10247255040*a(n-11) -65748533984*a(n-12) -63030407168*a(n-13) -647720099200*a(n-14) +440437613568*a(n-15) +13580263445504*a(n-16) -17409442856448*a(n-17) -69178882206720*a(n-18) +39729794551808*a(n-19) +99914217435136*a(n-20) +439834661814272*a(n-21) +852903138000896*a(n-22) -140783884140544*a(n-23) -4865360025616384*a(n-24) -5195592273887232*a(n-25) -2883648215318528*a(n-26) +10901288358772736*a(n-27) +23646372080123904*a(n-28) -8554321461379072*a(n-29) +6779331384705024*a(n-30) +13060018811174912*a(n-31) -85990483850952704*a(n-32) -31219512086888448*a(n-33) -68904850477285376*a(n-34) +150292794693386240*a(n-35) +199936390543179776*a(n-36) -144158928022798336*a(n-37) -81848676363796480*a(n-38) +16712989059055616*a(n-39) +36969429216526336*a(n-40) -9921992929050624*a(n-41) +246290604621824*a(n-42) for n>45

Example

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

Crossrefs

Sequence in context: A234028 A135647 A269025 * A207224 A207011 A206975

Adjacent sequences: A207228 A207229 A207230 * A207232 A207233 A207234

Keyword

nonn

Author

R. H. Hardin Feb 16 2012

Status

approved