A231459 Number of (n+1)X(3+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

14, 38, 100, 272, 741, 2093, 6036, 17569, 51839, 154480, 465438, 1413661, 4328633, 13343012, 41361410, 128843945, 402969212, 1264606727, 3979686619, 12552988405, 39670815296, 125565825987, 397948664649, 1262512053378, 4008798974159

Offset

1,1

Comments

Column 3 of A231463

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -9*a(n-2) -25*a(n-3) +25*a(n-4) +97*a(n-5) -17*a(n-6) -113*a(n-7) -439*a(n-8) +323*a(n-9) +944*a(n-10) -544*a(n-11) -1037*a(n-12) +219*a(n-13) +1442*a(n-14) +1134*a(n-15) -1588*a(n-16) -3424*a(n-17) +2459*a(n-18) +3725*a(n-19) -4906*a(n-20) -2178*a(n-21) +4656*a(n-22) +60*a(n-23) -1844*a(n-24) +1914*a(n-25) +1068*a(n-26) -1242*a(n-27) -655*a(n-28) +177*a(n-29) -12*a(n-30) -162*a(n-31) -54*a(n-32)

Example

Some solutions for n=6
..0..1..0..0....0..0..1..1....0..1..1..1....0..0..0..0....0..0..0..0
..1..0..1..0....1..1..0..0....0..0..1..1....0..0..0..0....1..1..1..1
..0..1..0..1....1..1..0..0....0..0..0..0....1..1..1..1....1..1..1..1
..1..0..1..0....1..1..0..0....2..2..0..0....1..1..1..1....1..1..1..1
..0..1..0..0....1..1..1..0....2..2..2..2....2..2..2..2....2..2..2..2
..1..0..0..0....1..1..0..0....3..3..2..2....2..2..2..2....2..2..2..2
..1..1..1..1....1..1..0..0....3..3..3..3....3..3..3..3....3..3..3..3

Crossrefs

Sequence in context: A142241 A186121 A231391 * A244702 A187086 A044091

Adjacent sequences: A231456 A231457 A231458 * A231460 A231461 A231462

Keyword

nonn

Author

R. H. Hardin, Nov 09 2013

Status

approved