A253038 Number of (n+2)X(2+2) 0..3 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order

341, 540, 998, 1866, 3894, 8340, 18180, 40264, 89212, 198458, 445860, 999676, 2237366, 5016646, 11269984, 25320924, 56833694, 127532734, 286483406, 643804434, 1445740702, 3245814338, 7290747006, 16380214556, 36791610106

Offset

1,1

Comments

Column 2 of A253044

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +15*a(n-4) -88*a(n-5) -107*a(n-6) +69*a(n-7) +208*a(n-8) +1570*a(n-9) +623*a(n-10) -2575*a(n-11) -6085*a(n-12) -12938*a(n-13) +8665*a(n-14) +33677*a(n-15) +47606*a(n-16) +37948*a(n-17) -135552*a(n-18) -192203*a(n-19) -136886*a(n-20) +93850*a(n-21) +716500*a(n-22) +430864*a(n-23) -588*a(n-24) -841362*a(n-25) -1722932*a(n-26) +53076*a(n-27) +397976*a(n-28) +1827456*a(n-29) +2007160*a(n-30) -1043680*a(n-31) +865480*a(n-32) -2408520*a(n-33) -2494080*a(n-34) -707600*a(n-35) -2686832*a(n-36) +6166048*a(n-37) +4181856*a(n-38) +1880160*a(n-39) -1085312*a(n-40) -10104640*a(n-41) -313024*a(n-42) +1998208*a(n-43) +3442688*a(n-44) +3872256*a(n-45) -4363008*a(n-46) -91648*a(n-47) +326656*a(n-48) +128000*a(n-49) +844800*a(n-50) -2213888*a(n-51) +593920*a(n-52) +1159168*a(n-53) -520192*a(n-54) -16384*a(n-55) -32768*a(n-56) +16384*a(n-57) for n>61

Example

Some solutions for n=4
..0..0..1..1....0..0..1..1....0..1..1..2....0..1..1..0....0..1..1..0
..2..0..2..2....1..1..0..0....2..2..1..1....2..2..1..2....0..2..0..2
..0..1..1..2....0..1..0..1....2..1..2..2....2..1..2..2....2..2..0..0
..2..1..1..0....0..2..2..1....3..2..2..1....3..1..1..0....0..0..2..2
..0..2..0..0....2..2..0..2....3..1..3..1....2..2..1..2....2..0..2..0
..2..2..1..1....0..0..2..2....1..1..3..3....2..1..2..2....2..1..1..0

Crossrefs

Sequence in context: A025353 A025345 A337715 * A271873 A001567 A178723

Adjacent sequences: A253035 A253036 A253037 * A253039 A253040 A253041

Keyword

nonn

Author

R. H. Hardin, Dec 26 2014

Status

approved